BEGIN:VCALENDAR
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CALSCALE:GREGORIAN
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BEGIN:VEVENT
SUMMARY:Alberto Elduque (University of Zaragoza\, Spain)
DTSTART:20230109T150000Z
DTEND:20230109T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/1
DESCRIPTION:Title: Te
nsor categories\, algebras\, and superalgebras\nby Alberto Elduque (Un
iversity of Zaragoza\, Spain) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nAfter reviewing the basic definitions of tensor cat
egories and the notion of semisimplification of symmetric tensor categorie
s\, it will be shown how the semisimplification of the category of represe
ntations of the cyclic group of order 3 over a field of characteristic 3 i
s naturally equivalent to the category of vector superspaces over this fie
ld. This allows to define a superalgebra starting with any algebra endowed
with an order 3 automorphism. As a noteworthy example\, the exceptional c
omposition superalgebras will be obtained\, in a systematic way\, from the
split octonion algebra.\n
LOCATION:https://researchseminars.org/talk/ENAAS/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Seidon Alsaody (Uppsala University\, Sweden)
DTSTART:20230116T150000Z
DTEND:20230116T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/2
DESCRIPTION:Title: Br
own algebras\, Freudenthal triple systems and exceptional groups over ring
s\nby Seidon Alsaody (Uppsala University\, Sweden) as part of European
Non-Associative Algebra Seminar\n\n\nAbstract\nExceptional algebraic grou
ps are intimately related to various classes of non-associative algebras:
for example\, octonion algebras are related to groups of type $G_2$ and $D
_4$\, and Albert algebras to groups of type $F_4$ and $E_6$. This can be u
sed\, on the one hand\, to give concrete descriptions of homogeneous space
s under these groups and\, on the other hand\, to parametrize isotopes of
these algebras using said homogeneous spaces. The key tools are provided b
y the machinery of torsors and faithfully flat descent\, working over arbi
trary commutative rings (sometimes assuming 2 and 3 to be invertible).\n\n
I will talk about recent work where we do this from Brown algebras and the
ir associated Freudenthal triple systems\, whose automorphism groups are o
f type $E_6$ and $E_7$\, respectively. I will hopefully be able to show ho
w algebraic and geometric properties come together in this picture.\n
LOCATION:https://researchseminars.org/talk/ENAAS/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Karel Dekimpe (Catholic University of Leuven\, Belgium)
DTSTART:20230123T150000Z
DTEND:20230123T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/3
DESCRIPTION:Title: Di
-semisimple Lie algebras and applications in post-Lie algebra structures\nby Karel Dekimpe (Catholic University of Leuven\, Belgium) as part of
European Non-Associative Algebra Seminar\n\n\nAbstract\nWe call a Lie alge
bra $\\mathfrak g$ di-semisimple if it can be written as a vector space su
m $\\mathfrak g = \\mathfrak s_1 + \\mathfrak s_2$\, where $\\mathfrak s_1
$ and $\\mathfrak s_2$ are semisimple subalgebras of $\\mathfrak g$ and we
say that $\\mathfrak g$ is strongly di-semisimple if $\\mathfrak g$ can
be written as a direct vector space sum of semisimple subalgebras. We will
show that complex strongly di-semisimple Lie algebras have to be semisimp
le themselves. \n\nWe will then use this result to show that if a pair of
complex Lie algebras $(\\mathfrak g\, \\mathfrak n)$ with $\\mathfrak g$ s
emisimple admits a so called post-Lie algebra structure\, then \n$\\mathfr
ak n$ must be isomorphic to $\\mathfrak g$. \n\nJoint work with Dietrich B
urde and Mina Monadjem.\n
LOCATION:https://researchseminars.org/talk/ENAAS/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Towers (Lancaster University\, UK)
DTSTART:20230130T150000Z
DTEND:20230130T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/4
DESCRIPTION:Title: Zi
nbiel algebras are nilpotent\nby David Towers (Lancaster University\,
UK) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nZin
biel algebras were introduced by Loday in 1995. They are the Koszul dual o
f Leibniz algebras and Lemaire proposed the name of Zinbiel\, which is obt
ained by writing Leibniz backwards. In this talk\, I will introduce some o
f their main properties\, including the fact that\, over any field\, they
are nilpotent.\n
LOCATION:https://researchseminars.org/talk/ENAAS/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clara Franchi (Catholic University of the Sacred Heart\, Italy)
DTSTART:20230206T150000Z
DTEND:20230206T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/5
DESCRIPTION:Title: Ax
ial algebras of Monster type\nby Clara Franchi (Catholic University of
the Sacred Heart\, Italy) as part of European Non-Associative Algebra Sem
inar\n\n\nAbstract\nExtending earlier work by Ivanov on Majorana algebras\
, axial algebras of Monster type were introduced in 2015 by Hall\, Rehren
and Shpectorov in order to axiomatise some key features of certain classes
of algebras related to large families of finite simple groups\, such as t
he weight-2 components of OZ-type vertex operator algebras\, Jordan algebr
as\, and Matsuo algebras. In this talk\, I'll review the definition of axi
al algebras and the major examples. Then I'll discuss the general classifi
cation problem of the 2-generated objects and\, time permitting\, show its
applications in some special cases related to the Monster.\n
LOCATION:https://researchseminars.org/talk/ENAAS/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Justin McInroy (University of Chester\, UK)
DTSTART:20230213T150000Z
DTEND:20230213T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/6
DESCRIPTION:Title: Cl
assifying quotients of the Highwater algebra\nby Justin McInroy (Unive
rsity of Chester\, UK) as part of European Non-Associative Algebra Seminar
\n\n\nAbstract\nAxial algebras are a class of non-associative algebras wit
h a strong natural link to groups and have recently received much attentio
n. They are generated by axes which are semisimple idempotents whose eige
nvectors multiply according to a so-called fusion law. Of primary interes
t are the axial algebras with the Monster type $(\\alpha\, \\beta)$ fusion
law\, of which the Griess algebra (with the Monster as its automorphism g
roup) is an important motivating example.\n\nBy previous work of Yabe\, an
d Franchi and Mainardis\, any symmetric 2-generated axial algebra of Monst
er type $(\\alpha\, \\beta)$ is either in one of several explicitly known
families\, or is a quotient of the infinite-dimensional Highwater algebra
$\\mathcal{H}$\, or its characteristic 5 cover $\\hat{\\mathcal{H}}$. We
complete this classification by explicitly describing the infinitely many
ideals and thus quotients of the Highwater algebra (and its cover). As a
consequence\, we find that there exist 2-generated algebras of Monster typ
e $(\\alpha\, \\beta)$ with any number of axes (rather than just $1\, 2\,
3\, 4\, 5\, 6\, \\infty$ as we knew before) and of arbitrarily large finit
e dimension.\n\n\nIn this talk\, we will begin with a reminder of axial al
gebras which were introduced last week.\n\n\nThis is joint work with:\nCla
ra Franchi\, Catholic University of the Sacred Heart\, Milan\nMario Mainar
dis\, University of Udine\n
LOCATION:https://researchseminars.org/talk/ENAAS/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kenji Iohara (University of Lyon\, France)
DTSTART:20230220T150000Z
DTEND:20230220T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/7
DESCRIPTION:Title: On
Elliptic Root Systems\nby Kenji Iohara (University of Lyon\, France)
as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn 1985
\, K. Saito introduced elliptic root systems as root systems belonging to
a real vector space $F$ equiped with a symmetric bilinear form $I$ with si
gnature $(l\, 2\, 0)$. Such root systems are studied in view of simply ell
iptic singularities which are surface singularities with a regular ellipti
c curve in its resolution. K. Saito had classified elliptic root systems $
R$ with its one dimensional subspace $G$ of the radical of $I$\, in the ca
se when $R/G \\subset F/G$ is a reduced affine root system. In our joint w
ork with A. Fialowski and Y. Saito\, we have completed its classification\
; we classified the pair $(R\,G)$ whose quotient $R/G \\subset F/G$ is a n
on-reduced affine root system. In this talk\, we give an overview of ellip
tic root sysems and describe some of the new root systems we have found.\n
LOCATION:https://researchseminars.org/talk/ENAAS/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dietrich Burde (University of Vienna\, Austria)
DTSTART:20230227T150000Z
DTEND:20230227T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/8
DESCRIPTION:Title: Pr
e-Lie algebra structures on reductive Lie algebras and etale affine repres
entations\nby Dietrich Burde (University of Vienna\, Austria) as part
of European Non-Associative Algebra Seminar\n\n\nAbstract\nEtale affine re
presentations of Lie algebras and algebraic groups arise in the context\no
f affine geometry on Lie groups\, operad theory\, deformation theory and Y
oung-Baxter equations.\nFor reductive groups\, every etale affine represen
tation is equivalent to a\nlinear representation and we obtain a special c
ase of a prehomogeneous representation.\nSuch representations have been cl
assified by Sato and Kimura in some cases. The induced\nrepresentation on
the Lie algebra level gives rise to a pre-Lie algebra structure on the\nLi
e algebra g of G. For a Lie group G\, a pre-Lie algebra structure on g cor
responds to a\nleft-invariant affine structure on G. This refers to a well
-known question by John Milnor from 1977\non the existence of complete lef
t-invariant affine structures on solvable Lie groups.\n\nWe present result
s on the existence of etale affine representations of reductive groups and
Lie algebras\nand discuss a related conjecture of V. Popov concerning fla
ttenable groups and linearizable\nsubgroups of the affine Cremona group.\n
LOCATION:https://researchseminars.org/talk/ENAAS/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Willem Adriaan De Graaf (University of Trento\, Italy)
DTSTART:20230306T150000Z
DTEND:20230306T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/9
DESCRIPTION:Title: Co
mputing the first Galois cohomology set of a reductive algebraic group
\nby Willem Adriaan De Graaf (University of Trento\, Italy) as part of Eur
opean Non-Associative Algebra Seminar\n\n\nAbstract\nIn classification pro
blems over the real field R first Galois cohomology sets play an important
role\, as they often make it possible to classify the orbits of a real Li
e group. In this talk\, we outline an algorithm to compute the first Galoi
s cohomology set $H^1(G\,R)$ of a complex reductive algebraic group G defi
ned over the real field R. The algorithm is in a large part based on compu
tations in the Lie algebra of G. This is joint work with Mikhail Borovoi.\
n
LOCATION:https://researchseminars.org/talk/ENAAS/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adela Latorre (Polytechnic University of Madrid\, Spain)
DTSTART:20230313T150000Z
DTEND:20230313T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/10
DESCRIPTION:Title: S
olvable Lie algebras with complex symplectic structures\nby Adela Lato
rre (Polytechnic University of Madrid\, Spain) as part of European Non-Ass
ociative Algebra Seminar\n\n\nAbstract\nLet $\\mathfrak g$ be a $2n$-dimen
sional solvable Lie algebra. A complex structure on $\\mathfrak g$ is an e
ndomorphism $J$ that satisfies $J^2=-Id$ and $N_J(X\,Y)=0$\, for every $X\
,Y\\in\\mathfrak g$\, being\n$$N_J(X\,Y):=[X\,Y]+J[JX\,Y]+J[X\,JY]-[JX\,JY
].$$ \nSuppose that $\\mathfrak g$ simultaneously admits a complex structu
re $J$ and a symplectic structure $\\omega$ (i.e.\, a closed $2$-form $\\o
mega\\in\\wedge^2\\mathfrak g^*$ such that $\\omega^n\\neq 0$). \nAlthough
$J$ and $\\omega$ are initially two unrelated structures\, one can ask fo
r an additional condition involving both of them.\nIn this sense\, the pai
r $(J\,\\omega)$ is said to be a complex symplectic structure if $J$ is sy
mmetric with respect to $\\omega$\, in the sense that $\\omega(JX\,Y)=\\om
ega(X\,JY)$\, for every $X\,Y\\in\\mathfrak g$.\nIn this talk\, we will pr
esent some methods to find certain types of solvable Lie algebras (such as
nilpotent or almost Abelian) admitting complex symplectic structures.\n
LOCATION:https://researchseminars.org/talk/ENAAS/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Duc-Khanh Nguyen (University at Albany\, USA)
DTSTART:20230320T150000Z
DTEND:20230320T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/11
DESCRIPTION:Title: A
generalization of the Murnaghan-Nakayama rule for K-k-Schur and k-Schur f
unctions\nby Duc-Khanh Nguyen (University at Albany\, USA) as part of
European Non-Associative Algebra Seminar\n\n\nAbstract\nWe introduce a gen
eralization of K-k-Schur functions and k-Schur functions via the Pieri rul
e. Then we obtain the Murnaghan-Nakayama rule for the generalized function
s. The rule are described explicitly in the cases of K-k-Schur functions a
nd k-Schur functions\, with concrete descriptions and algorithms for coeff
icients. Our work recovers the result of Bandlow\, Schilling\, and Zabrock
i for k-Schur functions\, and explains it as a degeneration of the rule fo
r K-k-Schur functions. In particular\, many other special cases promise to
be detailed in the future.\n
LOCATION:https://researchseminars.org/talk/ENAAS/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hamid Usefi (Memorial University of Newfoundland\, Canada)
DTSTART:20230327T150000Z
DTEND:20230327T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/12
DESCRIPTION:Title: P
olynomial identities\, group rings and enveloping algebras\nby Hamid U
sefi (Memorial University of Newfoundland\, Canada) as part of European No
n-Associative Algebra Seminar\n\n\nAbstract\nI will talk about the develop
ment of the theory of polynomial identities initiated by important questio
ns such as Burnside's asking if every finitely generated torsion group
is finite. The field was enriched by contributions of many great mathemati
cians. Most notably Lie rings methods were developed and used by Zelmanov
in the 1990s to give a positive solution to the restricted Burnside probl
em which awarded him the Fields medal. It has been of great interest to ex
pand the theory to other varieties of algebraic structures. In particular\
, I will review when a group algebra or enveloping algebra satisfy a polyn
omial identity.\n
LOCATION:https://researchseminars.org/talk/ENAAS/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Fairon (University of Paris-Saclay\, France)
DTSTART:20230410T150000Z
DTEND:20230410T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/13
DESCRIPTION:Title: A
round Van den Bergh's double brackets\nby Maxime Fairon (University of
Paris-Saclay\, France) as part of European Non-Associative Algebra Semina
r\n\n\nAbstract\nThe notion of a double Poisson bracket on an associative
algebra was introduced by M. Van den Bergh in order to induce a (usual) Po
isson bracket on the representation spaces of this algebra. I will start b
y reviewing the basics of this theory and its relation to other interestin
g operations\, such as Leibniz brackets and $H_0$-Poisson structures. I wi
ll then explain some recent results and generalisations related to double
Poisson brackets.\n
LOCATION:https://researchseminars.org/talk/ENAAS/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kaiming Zhao (Wilfrid Laurier University\, Waterloo\, Canada)
DTSTART:20230529T150000Z
DTEND:20230529T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/14
DESCRIPTION:Title: S
imple smooth modules\nby Kaiming Zhao (Wilfrid Laurier University\, Wa
terloo\, Canada) as part of European Non-Associative Algebra Seminar\n\n\n
Abstract\nLet L be a graded Lie algebra by integers with k-th homogenous s
pace $L_k$ where k are integers. An L-module V is called a smooth module i
f any vector in V can be annihilated by $L_k$ for all sufficiently large k
. Smooth modules for affine Kac-Moody algebras were introduced and studied
by Kazhdan and Lusztig in 1993. I will show why this class of modules sho
uld be studied and what results are known now. An easy characterization fo
r simple smooth modules for some Lie algebras will be provided.\n
LOCATION:https://researchseminars.org/talk/ENAAS/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marzia Mazzotta (University of Salento\, Italy)
DTSTART:20230417T150000Z
DTEND:20230417T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/15
DESCRIPTION:Title: C
lassification of set-theoretical solutions to the pentagon equation\nb
y Marzia Mazzotta (University of Salento\, Italy) as part of European Non-
Associative Algebra Seminar\n\n\nAbstract\nThe pentagon equation classical
ly originates from the field of Mathematical Physics. Our attention is pla
ced on the study of set-theoretical solutions of this equation\, namely\,
maps $s: X \\times X \\to X \\times X$ given by $s(x\, y)=(xy\, \\theta_x(
y))$\, where $X$ is a semigroup and $\\theta_x:X \\to X$ is a map satisfyi
ng two laws. In this talk\, we give some recent descriptions of some clas
ses of solutions achieved starting from particular semigroups. Into the sp
ecific\, we provide a characterization of \\emph{idempotent-invariant} sol
utions on a Clifford semigroup $X$\, that are those for which $\\theta_a$
remains invariant on the set of idempotents $E(X)$. In addition\, we will
focus on the classes of \\emph{involutive} and \\emph{idempotent} solution
s\, which are solutions fulfilling $s^2=id_{X \\times X}$ and $s^2=s$\, re
spectively.\n
LOCATION:https://researchseminars.org/talk/ENAAS/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Přemysl Jedlička (Czech University of Life Sciences\, Czechia)
DTSTART:20230403T150000Z
DTEND:20230403T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/16
DESCRIPTION:Title: N
on-degenerate involutive set-theoretic solutions of the Yang-Baxter equati
on of multipermutation level 2\nby Přemysl Jedlička (Czech Universit
y of Life Sciences\, Czechia) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nSet-theoretic solution of the Yang-Baxter equation
is a mapping $r:X\\times X\\to X\\times X$ satisfying\n\\[ (r\\times 1) (1
\\times r) (r\\times 1) = (1\\times r) (r\\times 1) (1\\times r). \\]\nA s
olution $r: (x\,y)\\mapsto (\\sigma_x(y)\,\\tau_y(x))$ is called non-degen
erate if the mappings $\\sigma_x$ and $\\tau_y$ are permutations\, for all
$x\,y\\in X$. A solution is called involutive if $r^2=1$.\n\nIf $(X\,r)$
is a non-degenerate involutive solution $(X\,r)$ then the relation~$\\sim$
defined by $x\\sim y\\equiv \\sigma_x=\\sigma_y$ is a congruence. A solut
ion is of multipermutation level 2 if $|(X/\\sim)/\\sim|=1$.\n\nIn our tal
k we focus on these solutions and we present several constructions and pro
perties.\n
LOCATION:https://researchseminars.org/talk/ENAAS/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Malihe Yousofzadeh (University of Isfahan\, Iran)
DTSTART:20230522T150000Z
DTEND:20230522T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/17
DESCRIPTION:Title: F
inite Weight Modules over Affine Lie Superalgebras\nby Malihe Yousofza
deh (University of Isfahan\, Iran) as part of European Non-Associative Alg
ebra Seminar\n\n\nAbstract\nNonzero real vectors of an affine Lie superalg
ebra act on a simple module either locally nilpotently or injectively. Thi
s helps us to divide simple finite weight modules over a twisted affine Li
e superalgebra $\\mathfrak{L}$ into two subclasses called hybrid and tight
. We will talk about the characterization as well as the classification pr
oblem of modules in each subclass. In this regard\, the classification of
bases of the root system of $\\mathfrak{L}$ is crucial. We will discuss ho
w we can classify the bases and how we can use the obtained classification
to study simple finite weight modules over $\\mathfrak{L}.$\n
LOCATION:https://researchseminars.org/talk/ENAAS/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yunhe Sheng (Jilin University\, China)
DTSTART:20230508T090000Z
DTEND:20230508T100000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/18
DESCRIPTION:Title: R
ota-Baxter operators and post-groups\nby Yunhe Sheng (Jilin University
\, China) as part of European Non-Associative Algebra Seminar\n\n\nAbstrac
t\nRota-Baxter operators on Lie algebras were first studied by Belavin\, D
rinfeld and Semenov-Tian-Shansky as operator forms of the classical Yang-B
axter equation. Integrating the Rota-Baxter operators on Lie algebras\, we
introduce the notion of Rota-Baxter operators on Lie groups and more gene
rally on groups. Then the factorization theorem can be achieved directly o
n groups. We introduce the notion of post-Lie groups\, whose differentiati
ons are post-Lie algebras. A Rota-Baxter operator on a group naturally ind
uces a post-group. Post-groups are also closely related to operads\, brace
s\, Lie-Butcher groups and various structures.\n
LOCATION:https://researchseminars.org/talk/ENAAS/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mátyás Domokos (Alfréd Rényi Institute of Mathematics\, Hungar
y)
DTSTART:20230508T150000Z
DTEND:20230508T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/19
DESCRIPTION:Title: A
n application of classical invariant theory to the study of identities and
concomitants of irreducible representations of the simple 3-dimensional c
omplex Lie algebra\nby Mátyás Domokos (Alfréd Rényi Institute of M
athematics\, Hungary) as part of European Non-Associative Algebra Seminar\
n\n\nAbstract\nTo an $n$-dimensional representation of a finite dimensiona
l Lie algebra one can naturally associate an algebra of equivariant polyno
mial maps from the space of $m$-tuples of elements of the Lie algebra into
the space of $n$-by-$n$ matrices. In the talk we mainly deal with the spe
cial case of irreducible\nrepresentations of the simple $3$-dimensional co
mplex Lie algebra\, and discuss results on the generators of the correspon
ding associative algebra of concomitants as well as results on the quantit
ative behaviour of the identities of these representations.\n
LOCATION:https://researchseminars.org/talk/ENAAS/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rutwig Campoamor Stursberg (Complutense University of Madrid\, Spa
in)
DTSTART:20230605T150000Z
DTEND:20230605T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/20
DESCRIPTION:Title: C
ommutants of subalgebras in universal enveloping algebras\nby Rutwig C
ampoamor Stursberg (Complutense University of Madrid\, Spain) as part of E
uropean Non-Associative Algebra Seminar\n\n\nAbstract\nThe problem of dete
rmining centralizers in the enveloping algebras of Lie algebras is conside
red from both the algebraic and analytical perspectives. Applications of t
he procedure\, such as the decomposition problem of the enveloping algebra
of a simple Lie algebra\, the labelling problem and the construction of o
rthonormal bases of states are considered.\n
LOCATION:https://researchseminars.org/talk/ENAAS/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lewis Topley (University of Bath\, UK)
DTSTART:20230515T090000Z
DTEND:20230515T100000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/21
DESCRIPTION:Title: M
odular representation theory and finite W-algebras\nby Lewis Topley (U
niversity of Bath\, UK) as part of European Non-Associative Algebra Semina
r\n\n\nAbstract\nFinite W-algebras were introduced by Premet in full gener
ality\, and they quickly became quite famous for their many applications i
n the representation theory of complex semisimple Lie algebras\, especiall
y the classification of primitive ideals. However\, these algebras first a
ppeared in the representation theory of Lie algebras associated to reducti
ve groups in positive characteristic. In this talk I will survey the histo
ry of finite W-algebras in modular representation theory\, and explain som
e of the contributions I have made to the field. The main applications in
this talk will be the construction and classification of``small'' modul
es of Lie algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thiago Castilho de Mello (Federal University of São Paulo\, Brazi
l)
DTSTART:20230424T150000Z
DTEND:20230424T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/22
DESCRIPTION:Title: I
mages of polynomials on algebras\nby Thiago Castilho de Mello (Federal
University of São Paulo\, Brazil) as part of European Non-Associative Al
gebra Seminar\n\n\nAbstract\nThe so-called Lvov-Kaplansky Conjecture state
s that the image of a multilinear polynomial evaluated on the matrix algeb
ra or order n is always a vector subspace. A solution to this problem is k
nown only for $n=2$. In this talk we will present analogous conjectures fo
r other associative and non-associative algebras and for graded algebras.
Also\, we will show how we can use gradings to present a statement equival
ent to the Lvov-Kaplansky conjecture.\n
LOCATION:https://researchseminars.org/talk/ENAAS/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandro Mattarei (University of Lincoln\, UK)
DTSTART:20230612T150000Z
DTEND:20230612T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/23
DESCRIPTION:Title: G
raded Lie algebras of maximal class\nby Sandro Mattarei (University of
Lincoln\, UK) as part of European Non-Associative Algebra Seminar\n\n\nAb
stract\nThe title matches that of a series of papers by various authors be
ginning in 1997\, whose goal was the study and classification of such alge
bras over fields of positive characteristic. The original motivation came
from group theory: the Leedham-Green and Newman coclass conjectures on pro
-p groups from 1980 had all become theorems relatively recently\, and subs
equent results of Shalev and Zelmanov had raised interest in what one coul
d say about Lie algebras of finite coclass. In positive characteristic\, t
he simplest case of coclass one (i.e.\, 'Lie algebras of maximal class'\,
also called 'filiform' in some quarters) appeared challenging even under t
he strong assumptions of those Lie algebras being infinite-dimensional and
graded over the positive integers. I will review motivations and results
of those studies\, including some classifications obtained by Caranti\, Ne
wman\, Vaughan-Lee. Then I will describe some generalizations recently est
ablished with three of my former PhD students.\n
LOCATION:https://researchseminars.org/talk/ENAAS/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Esther García González (King Juan Carlos University\, Spain)
DTSTART:20230626T150000Z
DTEND:20230626T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/24
DESCRIPTION:Title: N
ilpotent last-regular elements\nby Esther García González (King Juan
Carlos University\, Spain) as part of European Non-Associative Algebra Se
minar\n\n\nAbstract\nWe say that an element $x$ in a ring $R$ is nilpotent
last-regular if it is nilpotent of certain index $n+1$ and its last nonze
ro power $x^n$ is regular von Neumann\, i.e.\, there exists another elemen
t $y\\in R$ such that $x^nyx^n=x^n$. This type of elements naturally arise
when studying certain inner derivations in the Lie algebra $\\Skew(R\,*)$
of a ring $R$ with involution $*$ whose indices of nilpotence differ when
considering them acting as derivations on $\\Skew(R\,*)$ and on the whole
$R$. When moving to the symmetric Martindale ring of quotients $Q^s_m(R)$
of $R$ we still obtain inner derivations with the same indices of nilpote
nce on $Q^s_m(R)$ and on the skew-symmetric elements $\\Skew(Q^s_m(R)\,*)$
of $Q^s_m(R)$\, but with the extra condition of being generated by a nilp
otent last-regular element. This condition strongly determines the structu
re of $Q^s_m(R)$ and of $\\Skew(Q^s_m(R)\,*)$. \nWe will review the Jordan
canonical form of nilpotent last-regular elements and show how to get gra
dings in associative algebras (with and without involution) when they have
such elements.\n
LOCATION:https://researchseminars.org/talk/ENAAS/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sigiswald Barbier (Ghent University\, Belgium)
DTSTART:20230703T150000Z
DTEND:20230703T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/25
DESCRIPTION:Title: D
iagram categories of Brauer type\nby Sigiswald Barbier (Ghent Universi
ty\, Belgium) as part of European Non-Associative Algebra Seminar\n\n\nAbs
tract\nDiagram categories are a special kind of tensor categories that can
be represented using diagrams. In this talk I will give an introduction t
o categories represented using Brauer diagrams. In particular I will expla
in the relation with the Brauer algebra and how the categorical framework
can be applied to representation theory of the corresponding algebra.\n
LOCATION:https://researchseminars.org/talk/ENAAS/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Arzhantsev (HSE University\, Russia)
DTSTART:20230515T150000Z
DTEND:20230515T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/26
DESCRIPTION:Title: U
niqueness of addition in Lie algebras\nby Ivan Arzhantsev (HSE Univers
ity\, Russia) as part of European Non-Associative Algebra Seminar\n\n\nAbs
tract\nWe say that a Lie ring R is called a unique addition Lie ring\, or
briefly a UA-Lie ring\, if any commutator-preserving bijection on R preser
ves the addition as well. We prove that any semisimple Lie algebra and any
its parabolic subalgebra is a UA-Lie ring. Also we describe wide classes
of solvable UA-Lie rings.\n
LOCATION:https://researchseminars.org/talk/ENAAS/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Dotsenko (University of Strasbourg\, France)
DTSTART:20230424T090000Z
DTEND:20230424T100000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/27
DESCRIPTION:Title: O
perad filtrations and quantization\nby Vladimir Dotsenko (University o
f Strasbourg\, France) as part of European Non-Associative Algebra Seminar
\n\n\nAbstract\nThe celebrated problem of deformation quantization discuss
es deformations of Poisson algebras into associative algebras\, a question
that is\, in the end\, motivated by quantum mechanics. I shall discuss th
is question and some of its generalisations from the purely algebraic poin
t of view using the theory of operads. In particular\, I shall show how to
prove that there are\, in a strict mathematical sense\, only two meaningf
ul deformation problems for Poisson algebras\, namely deforming them in th
e class of all Poisson algebras or all associative algebras\, and there is
only one meaningful deformation problem for the so called almost Poisson
algebras (also sometimes known as generic Poisson algebras)\, namely defor
ming them in the class of all almost Poisson algebras. For instance\, this
explains the existing body of work in the mathematical physics literature
asserting that some classes of non-associative star products cannot be al
ternative\, are always flexible etc.\n
LOCATION:https://researchseminars.org/talk/ENAAS/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Csaba Schneider (Federal University of Minas Gerais\, Brazil)
DTSTART:20230821T150000Z
DTEND:20230821T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/28
DESCRIPTION:Title: C
omputing invariants of some nilpotent Lie algebras\nby Csaba Schneider
(Federal University of Minas Gerais\, Brazil) as part of European Non-Ass
ociative Algebra Seminar\n\n\nAbstract\nI will present some interesting co
mputations concerning polynomial and rational invariants of nilpotent Lie
algebras. I will say more about standard filiform Lie algebras which appea
r to have the highest level of complication among the small-dimensional al
gebras. I will outline an implementable algorithm for the computation of g
enerators of the field of rational invariants.\n
LOCATION:https://researchseminars.org/talk/ENAAS/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alberto Facchini (University of Padua\, Italy)
DTSTART:20230814T150000Z
DTEND:20230814T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/29
DESCRIPTION:Title: H
eaps and trusses\nby Alberto Facchini (University of Padua\, Italy) as
part of European Non-Associative Algebra Seminar\n\n\nAbstract\nI will pr
esent the first notions concerning heaps and trusses. Heaps were introduce
d for the first time by H. Prüfer (1924) and R. Baer (1929). A heap is a
pair $(H\, [−\,−\,−])$ consisting of a set $H$ and a ternary operat
ion $$[−\,−\,−] : H \\times H \\times H \\to H\, (x\, y\, z) \\to
[x\, y\, z]\,$$ such that\, for all $v\, w\, x\, y\, z \\in H\,$ \n$$[v\
, w\, [x\, y\, z]] = [[v\, w\, x\, ]\, y\, z]\, \\ [x\, x\, y] = y\,\\ [y\
, x\, x]= y.$$\n Truss is a much more recent algebraic structure (T. Brzez
iński\, 2019). A truss is a heap with a further associative binary opera
tion\, denoted by juxtaposition\, which distributes over $[−\,−\,−]\
,$ that is\, for all $w\, x\, y\, z \\in T\,$ \n$$w[x\, y\, z] = [wx\, wy\
, wz]\, \\ [x\, y\, z]w = [xw\, yw\, zw]\,\\ [x\, y\, z] =[z\, y\, x].$$\n
LOCATION:https://researchseminars.org/talk/ENAAS/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elitza Hristova (Institute of Mathematics and Informatics\, Bulgar
ia)
DTSTART:20230828T150000Z
DTEND:20230828T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/30
DESCRIPTION:Title: O
n the GL(n)-module structure of Lie nilpotent associative relatively free
algebras\nby Elitza Hristova (Institute of Mathematics and Informatics
\, Bulgaria) as part of European Non-Associative Algebra Seminar\n\n\nAbst
ract\nLet $K\\langle X\\rangle$ denote the free associative algebra genera
ted by a finite set $X$ with n elements over a field $K$ of characteristic
0. Let $I_p$ denote the two-sided associative ideal in $K\\langle X\\rang
le$ generated by all commutators of length $p$\, where $p$ is an arbitrary
positive integer greater than 1. The group ${\\rm GL(n)}$ acts in a natur
al way on the quotient $K\\langle X\\rangle/I_p$ and the ${\\rm GL(n)}$-mo
dule structure of $K\\langle X\\rangle/I_p$ is known for $p=2\,3\,4\,5$. I
n this talk\, we give some results on the ${\\rm GL}(n)$-module structure
of $K\\langle X\\rangle/I_p$ for any $p$. More precisely\, we give a bound
on the values of the highest weights of irreducible ${\\rm GL}(n)$-module
s which appear in the decomposition of $K\\langle X\\rangle/I_p$. We discu
ss also applications of these results related to the algebras of G-invaria
nts in $K\\langle X\\rangle/I_p$\, where G is one of the classical ${\\rm
GL}(n)$-subgroups ${\\rm SL}(n)$\, ${\\rm O}(n)$\, ${\\rm SO}(n)$\, or ${\
\rm Sp}(2k)$ (for $n=2k$).\n
LOCATION:https://researchseminars.org/talk/ENAAS/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tiago Macedo (Federal University of São Paulo\, Brazil)
DTSTART:20230710T150000Z
DTEND:20230710T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/31
DESCRIPTION:Title: F
inite-dimensional modules for map superalgebras\nby Tiago Macedo (Fede
ral University of São Paulo\, Brazil) as part of European Non-Associative
Algebra Seminar\n\n\nAbstract\nIn this talk we will present recent result
s on the category of finite-dimensional modules for map superalgebras. Fir
stly\, we will show a new description of certain irreducible modules. Seco
ndly\, we will use this new description to extract homological properties
of the category of finite-dimensional modules for map superalgebras\, most
importantly\, its block decomposition.\n
LOCATION:https://researchseminars.org/talk/ENAAS/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Solotar (University of Buenos Aires\, Argentina)
DTSTART:20230724T150000Z
DTEND:20230724T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/32
DESCRIPTION:Title: T
amarkin-Tsygan calculus for gentle algebras\nby Andrea Solotar (Univer
sity of Buenos Aires\, Argentina) as part of European Non-Associative Alge
bra Seminar\n\n\nAbstract\nThe whole structure given by the Hochschild coh
omology and homology of an associative algebra A together with the cup and
cap products\, the Gerstenhaber bracket and the Connes differential is ca
lled the Tamarkin-Tsygan calculus. It is invariant under derived equivalen
ce and if we can compute all these invariants provides a lot of informatio
n. The calculation of the whole Tamarkin-Tsygan calculus is very difficult
and generally not even possible for particular algebras. However\, there
exist some calculations for individual algebras. The problem is\, in gener
al\, that the minimal projective bimodule resolutions are difficult to fin
d and even if one is able to compute such a resolution\, it might be so co
mplicated that the computation of the Tamarkin-Tsygan calculus is not with
in reach. For monomial algebras the minimal projective bimodule resolution
is known and in the case of quadratic monomial algebras it is simple enou
gh\, to embark on the extensive calculations of the Tamarkin Tsygan calcul
us. Yet even for quadratic monomial algebras\, the combinatorial level of
the calculations is such\nthat it is too complicated to calculate the whol
e calculus. On the other hand for gentle algebras\, the additional constra
ints on their structure are such that the calculations become possible. We
will focus on the concrete aspects of these calculations.\n
LOCATION:https://researchseminars.org/talk/ENAAS/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexey Petukhov (Institute for Information Transmission Problems\,
Russia)
DTSTART:20230717T150000Z
DTEND:20230717T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/33
DESCRIPTION:Title: W
itt Lie algebra and the associated primitive ideals\nby Alexey Petukho
v (Institute for Information Transmission Problems\, Russia) as part of Eu
ropean Non-Associative Algebra Seminar\n\n\nAbstract\nIn my talk I would l
ike to discuss my joint articles with S. Sierra about the primitive ideals
of universal enveloping U(W) and the symmetric algebra S(W) of Witt Lie a
lgebra W and similar Lie algebras (including Virasoro Lie algebra). The ke
y theorem in this setting is that every nontrivial quotient by a two-sided
ideal of U(W) or S(W) has finite Gelfand-Kirillov dimension. Together wit
h S. Sierra we enhanced this statement to the description of primitive Poi
sson ideals of S(W) in terms of certain points on the complex plane plus a
few parameters attached to these points. In the end I will try to explain
how all these concepts works for the ideals whose quotient has Gelfand-Ki
rillov dimension 2.\n
LOCATION:https://researchseminars.org/talk/ENAAS/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Şehmus Fındık (Çukurova University\, Turkey)
DTSTART:20230731T150000Z
DTEND:20230731T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/34
DESCRIPTION:Title: S
ymmetric polynomials in some certain noncommutative algebras\nby Şehm
us Fındık (Çukurova University\, Turkey) as part of European Non-Associ
ative Algebra Seminar\n\n\nAbstract\nLet F be a finitely generated free al
gebra in a variety of algebras over a field of characteristic zero. A poly
nomial in F is called symmetric if it is preserved under any permutation o
f the generators. The set S(F) of symmetric polynomials is a subalgebra of
F. In this talk\, we examine the algebras S(F)\, where F is the free meta
belian associative\, Lie\, Leibniz\, Poisson algebra or the free algebra g
enerated by generic traceless matrices or the free algebra in the variety
generated by Grassmann algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lleonard Rubio y Degrassi (Uppsala University\, Sweden)
DTSTART:20230807T150000Z
DTEND:20230807T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/35
DESCRIPTION:Title: H
ochschild cohomology groups under gluing idempotents\nby Lleonard Rubi
o y Degrassi (Uppsala University\, Sweden) as part of European Non-Associa
tive Algebra Seminar\n\n\nAbstract\nStable equivalences occur frequently i
n the representation theory of finite-dimensional algebras\; however\, the
se equivalences are poorly understood. An interesting class of stable equi
valences is obtained by ‘gluing’ two idempotents. More precisely\, let
A be a finite-dimensional algebra with a simple projective module and a s
imple injective module. Assume that B is a subalgebra of A having the same
Jacobson radical. Then B is constructed by identifying the two idempotent
s belonging to the simple projective module and to the simple injective mo
dule\, respectively. \n\nIn this talk\, we will compare the first Hochschi
ld cohomology groups of finite-dimensional monomial algebras under gluing
two arbitrary idempotents (hence not necessarily inducing a stable equival
ence). As a corollary\, we will show that stable equivalences obtained by
gluing two idempotents provide 'some functoriality' to the first Hochschil
d cohomology\, that is\, HH^1(A) is isomorphic to a quotient of HH^1(B).\n
LOCATION:https://researchseminars.org/talk/ENAAS/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mykola Khrypchenko (Univesity of Porto\, Portugal)
DTSTART:20230904T150000Z
DTEND:20230904T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/36
DESCRIPTION:Title: T
ransposed Poisson structures\nby Mykola Khrypchenko (Univesity of Port
o\, Portugal) as part of European Non-Associative Algebra Seminar\n\n\nAbs
tract\nA transposed Poisson algebra is a triple (L\,⋅\,[⋅\,⋅]) consi
sting of a vector space L with two bilinear operations ⋅ and [⋅\,⋅]\
, such that (L\,⋅) is a commutative associative algebra\; (L\,[⋅\,⋅]
) is a Lie algebra\; the "transposed" Leibniz law holds: 2z⋅[x\,y]=[z⋅
x\,y]+[x\,z⋅y] for all x\,y\,z∈L. A transposed Poisson algebra structu
re on a Lie algebra (L\,[⋅\,⋅]) is a (commutative associative) multipl
ication ⋅ on L such that (L\,⋅\,[⋅\,⋅]) is a transposed Poisson al
gebra. I will give an overview of my recent results in collaboration with
Ivan Kaygorodov (Universidade da Beira Interior) on classification of tran
sposed Poisson structures on several classes of Lie algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bauyrzhan Sartayev (Suleyman Demirel University\, Kazakhstan)
DTSTART:20230911T150000Z
DTEND:20230911T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/37
DESCRIPTION:Title: B
inary perm algebras and alternative algebras\nby Bauyrzhan Sartayev (S
uleyman Demirel University\, Kazakhstan) as part of European Non-Associati
ve Algebra Seminar\n\n\nAbstract\nWe describe the defining identities of a
variety of binary perm algebras which is a subvariety of the variety of a
lternative algebras. Moreover\, we construct a basis of the free binary pe
rm algebra. In addition\, we describe the subalgebras of binary perm algeb
ras under commutator which has a connection with Malcev algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hader Elgendy (Damietta University\, Egypt)
DTSTART:20230925T150000Z
DTEND:20230925T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/38
DESCRIPTION:Title: O
n Jordan quadruple systems\nby Hader Elgendy (Damietta University\, Eg
ypt) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nWe
present the recent results on Jordan quadruple systems. We show the Peirc
e decomposition for a Jordan quadruple system with respect to a quadripote
nt. We extend the notions of the orthogonality\, primitivity\, and minimal
ity of tripotents in a Jordan triple system to that of quadripotents\nin a
Jordan quadruple system. We show the relation between minimal and primiti
ve quadripotents in a Jordan quadruple system. We also discuss the results
on complemented subsystems of Jordan quadruple systems.\n
LOCATION:https://researchseminars.org/talk/ENAAS/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alfilgen Sebandal (Mindanao State University\, Philippines)
DTSTART:20231002T150000Z
DTEND:20231002T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/39
DESCRIPTION:Title: F
inite graded classification conjecture for Leavitt path algebras\nby A
lfilgen Sebandal (Mindanao State University\, Philippines) as part of Euro
pean Non-Associative Algebra Seminar\n\n\nAbstract\nGiven a directed graph
\, one can associate two algebraic entities: the Leavitt path algebra and
the talented monoid. The Graded Classification conjecture states that the
talented monoid could be a graded invariant for the Leavitt path algebra\,
i.e.\, isomorphism in the talented monoids reflects as graded equivalence
in the category of graded modules over the Leavitt path algebra of the co
rresponding directed graphs. In this talk\, we shall see confirmations of
this invariance in the ideal structure of the talented monoid with the so-
called Gelfand-Kirillov Dimension of the Leavitt path algebra. The last pa
rt of the talk is an affirmation of the Graded classification conjecture i
n the finite-dimensional case. This is a compilation of joint works with R
oozbeh Hazrat\, Wolfgang Bock\, and Jocelyn P. Vilela.\n
LOCATION:https://researchseminars.org/talk/ENAAS/39/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Chapman (Academic College of Tel-Aviv-Yaffo\, Israel)
DTSTART:20230918T150000Z
DTEND:20230918T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/40
DESCRIPTION:Title: R
oots and Critical Points of Cayley-Dickson Algebras\nby Adam Chapman (
Academic College of Tel-Aviv-Yaffo\, Israel) as part of European Non-Assoc
iative Algebra Seminar\n\n\nAbstract\n"We study the roots and critical poi
nts (i.e.\, points at which the formal derivative vanishes) of standard po
lynomials over Cayley-Dickson algebras.\nIn the anisotropic real case\, we
prove that the critical points live inside the convex hull of the roots o
f the polynomial.\nThe talk is based on joint work with Alexander Guterman
\, Solomon Vishkautsan and Svetlana Zhilina."\n
LOCATION:https://researchseminars.org/talk/ENAAS/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Petr Vojtěchovský (University of Denver\, USA)
DTSTART:20231030T150000Z
DTEND:20231030T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/41
DESCRIPTION:Title: S
olvability and nilpotence just beyond groups\nby Petr Vojtěchovský (
University of Denver\, USA) as part of European Non-Associative Algebra Se
minar\n\n\nAbstract\nSolvability and nilpotence arise naturally from the c
ommutator theory in congruence modular varieties. In the presence of assoc
iativity\, the resulting concepts agree with the classical concepts of gro
up theory. But the two kinds of solvability differ in loops ( = not necess
arily associative groups) and it is a difficult question to determine the
boundary where the two theories coincide. I will review the general theory
and report on recent results\, particularly in Moufang loops. For instanc
e\, we will prove the Odd Order Theorem for Moufang loops for the stronger
notion of solvability. This is joint work with Ales Drapal and David Stan
ovsky.\n
LOCATION:https://researchseminars.org/talk/ENAAS/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Gorbatsevich (Russian State Technological University name
d after K.E. Tsiolkovky\, Russia)
DTSTART:20231009T150000Z
DTEND:20231009T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/42
DESCRIPTION:Title: O
n some classes of bases in finite-dimensional Lie algebras\nby Vladimi
r Gorbatsevich (Russian State Technological University named after K.E. Ts
iolkovky\, Russia) as part of European Non-Associative Algebra Seminar\n\n
\nAbstract\nLie algebras having bases of a special form (nice and beautifu
l bases) are considered. For nice bases\, it is proved that in any nilpote
nt Lie algebra their number (up to equivalence) is finite. For some Lie a
lgebras of low dimension\, it is shown that\, when passing from a complex
Lie algebra to its realification\, the property to have a beautiful basis
is lost. Also nilpotent Lie algebras of dimensions less than 8 are consid
ered.\n
LOCATION:https://researchseminars.org/talk/ENAAS/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Markl (The Czech Academy of Sciences\, Czechia)
DTSTART:20231023T150000Z
DTEND:20231023T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/43
DESCRIPTION:Title: T
ransfers of strongly homotopy structures as Grothendieck bifibrations\
nby Martin Markl (The Czech Academy of Sciences\, Czechia) as part of Euro
pean Non-Associative Algebra Seminar\n\n\nAbstract\nIt is well-known that
strongly homotopy structures can be transferred over chain homotopy equiva
lences. Using the uniqueness results of Markl & Rogers we show that the tr
ansfers could be organized into a discrete Grothendieck bifibration. An im
mediate aplication is e.g. functoriality up to isotopy.\n
LOCATION:https://researchseminars.org/talk/ENAAS/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guodong Zhou (East China Normal University\, China)
DTSTART:20231016T150000Z
DTEND:20231016T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/44
DESCRIPTION:Title: T
he homotopy theory of operated algebras\nby Guodong Zhou (East China N
ormal University\, China) as part of European Non-Associative Algebra Semi
nar\n\n\nAbstract\nThe talk is a survey of our recent results on the homot
opy theory of operated algebras such as Rota-Baxter associative (or Lie) a
lgebras and differential associative (or Lie) algebras etc. We make explic
it the Kozul dual homotopy cooperads and the minimal models of the operads
governing these operated algebras. As a consequence the L-infinity struct
ures on the deformation complexes are described as well.\n
LOCATION:https://researchseminars.org/talk/ENAAS/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:František Marko (Pennsylvania State University\, USA)
DTSTART:20231113T150000Z
DTEND:20231113T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/45
DESCRIPTION:Title: B
locks of rational supermodules over some quasi-reductive supergroups in po
sitive characteristic\nby František Marko (Pennsylvania State Univers
ity\, USA) as part of European Non-Associative Algebra Seminar\n\n\nAbstra
ct\nThis is an overview of joint work with Alexandr N. Zubkov. We discuss
linkage principles and blocks for general linear\, ortho-symplectic\, and
periplectic supergroups over fields of positive characteristics. In the en
d\, we describe the strong linkage principle and blocks for the queer supe
rgroup Q(2)."\n
LOCATION:https://researchseminars.org/talk/ENAAS/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Senne Trappeniers (Free University of Brussels\, Belgium)
DTSTART:20231127T150000Z
DTEND:20231127T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/46
DESCRIPTION:Title: T
he interplay between skew braces\, the Yang–Baxter equation and Hopf–G
alois structures\nby Senne Trappeniers (Free University of Brussels\,
Belgium) as part of European Non-Associative Algebra Seminar\n\n\nAbstract
\nIn 2007\, Wolfgang Rump introduced algebraic objects called braces\, the
se gen- eralise Jacobson radical rings and are related to involutive non-d
egenerate set- theoretic solutions of the Yang–Baxter equation (YBE). Th
ese objects were subse- quently generalised to skew braces by Leandro Guar
nieri and Leandro Vendramin in 2017\, and a similar relation was shown to
hold for non-degenerate set-theoretic solutions of the YBE which are not n
ecessarily involutive. In this talk\, we will de- scribe this interplay be
tween skew braces and the YBE. We will also discuss their relation to Hopf
–Galois structures and see how this extends the classical Galois theory
in an elegant way.\n
LOCATION:https://researchseminars.org/talk/ENAAS/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Svetlana Zhilina (Lomonosov Moscow State University\, Russia)
DTSTART:20231106T150000Z
DTEND:20231106T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/47
DESCRIPTION:Title: O
n the lengths of Okubo algebras\nby Svetlana Zhilina (Lomonosov Moscow
State University\, Russia) as part of European Non-Associative Algebra Se
minar\n\n\nAbstract\nThe length function of a non-associative algebra desc
ribes the guaranteed number of multiplications which will be sufficient to
generate the whole algebra with its arbitrary generating set. In this tal
k we present a new method for length computation based on the sequence of
differences between the dimensions of a certain sequence of subspaces. It
allows us to compute the length of an Okubo algebra A over an arbitrary fi
eld. Namely\, if A contains either nonzero idempotents or zero divisors\,
then its length equals four\, and otherwise its length equals three. We al
so show that\, in the latter case\, A is generated by any two elements whi
ch do not belong to the same two-dimensional subalgebra. The talk is based
on a joint work with Alexander Guterman.\n
LOCATION:https://researchseminars.org/talk/ENAAS/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Lopatin (University of Campinas\, Brazil)
DTSTART:20231120T150000Z
DTEND:20231120T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/48
DESCRIPTION:Title: P
olynomial invariants for two dimensional algebras\nby Artem Lopatin (U
niversity of Campinas\, Brazil) as part of European Non-Associative Algebr
a Seminar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/48/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Amir Fernández Ouaridi (University of Coimbra\, Portugal)
DTSTART:20231204T150000Z
DTEND:20231204T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/49
DESCRIPTION:Title: O
n the simple transposed Poisson algebras and Jordan superalgebras\nby
Amir Fernández Ouaridi (University of Coimbra\, Portugal) as part of Euro
pean Non-Associative Algebra Seminar\n\n\nAbstract\nWe prove that a transp
osed Poisson algebra is simple if and only if its associated Lie bracket i
s simple. Consequently\, any simple finite-dimensional transposed Poisson
algebra over an algebraically closed field of characteristic zero is trivi
al. Similar results are obtained for transposed Poisson superalgebras. An
example of a non-trivial simple finite-dimensional transposed Poisson alge
bra is constructed by studying the transposed Poisson structures on the mo
dular Witt algebra. Furthermore\, we show that the Kantor double of a tran
sposed Poisson algebra is a Jordan superalgebra\, that is\, we prove that
transposed Poisson algebras are Jordan brackets. Additionally\, a simplic
ity criterion for the Kantor double of a transposed Poisson algebra is obt
ained.\n
LOCATION:https://researchseminars.org/talk/ENAAS/49/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Susanne Pumpluen (University of Nottingham\, UK)
DTSTART:20231211T150000Z
DTEND:20231211T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/50
DESCRIPTION:Title: A
way to generalize classical results from central simple algebras to the n
onassociative setting\nby Susanne Pumpluen (University of Nottingham\,
UK) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nRe
cently\, the theory of semiassociative algebras and their Brauer monoid wa
s introduced by Blachar\, Haile\, Matri\, Rein\, and Vishne as a canoni
cal generalization of the theory of associative central simple algebras an
d their Brauer group: together with the tensor product semiassociative alg
ebras over a field form a monoid that contains the classical Brauer group
as its unique maximal subgroup. We present classes of semiassociative alge
bras that are canonical generalizations of classes of certain central simp
le algebras and explore their behaviour in the Brauer monoid. Time permitt
ing\, we also discuss some - hopefully interesting - particularities of th
is newly defined Brauer monoid.\n
LOCATION:https://researchseminars.org/talk/ENAAS/50/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergio López-Permouth (Ohio University\, USA)
DTSTART:20240108T150000Z
DTEND:20240108T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/51
DESCRIPTION:Title: B
asic Extension Modules (All bases are created equal\, but some are more eq
ual than others)\nby Sergio López-Permouth (Ohio University\, USA) as
part of European Non-Associative Algebra Seminar\n\n\nAbstract\nWe report
on ongoing research about a module-theoretic construction which\, when su
ccessful\, yields natural extensions of infinite dimensional modules over
arbitrary algebras. Whether the construction works or not depends on the b
asis that one chooses to carry on such a construction. Bases that work are
said to be amenable. A natural example on which one may focus is when the
module is the algebra itself. For instance\, a great deal of the work don
e so far has focused on infinite dimensional algebra of polynomials on a s
ingle variable. We will see that amenability and related notions serve to
classify the distinct bases according to interesting complementary propert
ies having to do with the types of relations induced on them by the proper
ties of their change-of-basis matrices.\n
LOCATION:https://researchseminars.org/talk/ENAAS/51/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vladimir Tkachev (Linköping University\, Sweden)
DTSTART:20240115T150000Z
DTEND:20240115T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/52
DESCRIPTION:Title: S
ome questions of nonassociative algebra from the idempotent point of view<
/a>\nby Vladimir Tkachev (Linköping University\, Sweden) as part of Europ
ean Non-Associative Algebra Seminar\n\n\nAbstract\nHow to recover an algeb
ra structure if the algebra does NOT satisfy any reasonable identity? How
to characterize its idempotents\, their spectrum\, or fusion laws? In my t
alk\, I will discuss what can be thought of as "nonassociative algebra in
large"\, imitating a well-known concept of "geometry in large". In other w
ords\, the properties of nonassociative algebras which crucially depend on
a complete set of idempotents. The latter is very related to the concept
of generic algebras. I will explain some recent results in this direction
and some unsolved problems.\n
LOCATION:https://researchseminars.org/talk/ENAAS/52/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Friedrich Wagemann (University of Nantes\, France)
DTSTART:20240122T150000Z
DTEND:20240122T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/53
DESCRIPTION:Title: C
ohomology of semi-direct product Lie algebras\nby Friedrich Wagemann (
University of Nantes\, France) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nThis is joint work with Dietrich Burde (University
of Vienna\, Austria). Intrigued by computations of Richardson\, our goal
is to compute the adjoint cohomology spaces of Lie algebras which are the
semi-direct product of a simple Lie algebra s and an s-module. We present
some theorems and conjectures in these cohomologies.\n
LOCATION:https://researchseminars.org/talk/ENAAS/53/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yanyong Hong (Hangzhou Normal University\, China)
DTSTART:20240129T150000Z
DTEND:20240129T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/54
DESCRIPTION:Title: N
ovikov bialgebras\, infinite-dimensional Lie bialgebras and Lie conformal
bialgebras\nby Yanyong Hong (Hangzhou Normal University\, China) as pa
rt of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk
\, I will introduce a bialgebra theory for the Novikov algebra\, namely th
e Novikov bialgebra\, which is characterized by the fact that its affiniza
tion (by a quadratic right Novikov algebra) gives an infinite-dimensional
Lie bialgebra. A Novikov bialgebra is also characterized as a Manin triple
of Novikov algebras. The notion of Novikov Yang-Baxter equation is introd
uced\, whose skewsymmetric solutions can be used to produce Novikov bialge
bras and hence Lie bialgebras. These solutions also give rise to skewsymme
tric solutions of the classical Yang-Baxter equation in the infinite-dimen
sional Lie algebras from the Novikov algebras. Moreover\, a similar connec
tion between Novikov bialgebras and Lie conformal bialgebras will be intro
duced. This talk is based on joint works with Chengming Bai and Li Guo.\n
LOCATION:https://researchseminars.org/talk/ENAAS/54/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucas Buzaglo (University of Edinburgh\, UK)
DTSTART:20240205T150000Z
DTEND:20240205T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/55
DESCRIPTION:Title: D
erivations\, extensions\, and rigidity of subalgebras of the Witt algebra<
/a>\nby Lucas Buzaglo (University of Edinburgh\, UK) as part of European N
on-Associative Algebra Seminar\n\n\nAbstract\nWe study Lie algebraic prope
rties of subalgebras of the Witt algebra and the one-sided Witt algebra: w
e compute derivations\, one-dimensional extensions\, and automorphisms of
these subalgebras. In particular\, all these properties are inherited from
the full Witt algebra (e.g. derivations of subalgebras are simply restric
tions of derivations of the Witt algebra). We also prove that any isomorph
ism between subalgebras of finite codimension extends to an automorphism o
f the Witt algebra. We explain this "rigid" behavior by proving a universa
l property satisfied by the Witt algebra as a completely non-split extensi
on of any of its subalgebras of finite codimension. This is a purely Lie a
lgebraic property which I will introduce in the talk.\n
LOCATION:https://researchseminars.org/talk/ENAAS/55/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Saïd Benayadi (University of Lorraine\, France)
DTSTART:20240212T150000Z
DTEND:20240212T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/56
DESCRIPTION:Title: O
n a class of pseudo-Euclidean left-symmetric algebras\nby Saïd Benaya
di (University of Lorraine\, France) as part of European Non-Associative A
lgebra Seminar\n\n\nAbstract\nA pseudo-Euclidean left-symmetric algebra $(
A\, .\,< \, >)$ is a real left-symmetric algebra $(A\,.)$ endowed with a n
on-degenerate symmetric bilinear form $< \, >$ such that left multiplicat
ions by any element of A are skew-symmetric with respect to $< \, >$. We r
ecall that a pseudo-Euclidean Lie algebra $(g\, [ \, ]\, < \, >)$ is flat
if and only if $(g\, .\, \,< \, >)$ its underlying vector space endowed w
ith the Levi-Civita product associated with $< \, >$ is a pseudo-Euclidean
left-symmetric algebra. In this talk\, We will give an inductive classifi
cation of pseudo-Euclidean left-symmetric algebras $(A\, .\,< \, >)$ such
that commutators of allelements of A are contained in the left annihilato
r of $(A\, .)\,$ these algebras will be called pseudo-Euclidean left-symme
tric L−algebras of any signature. To do this\, we will develop double ex
tension processes that allow us to have inductive descriptions of all pseu
do-Euclidean left-symmetric $L$−algebras and of all its pseudo-Euclidean
modules.\n
LOCATION:https://researchseminars.org/talk/ENAAS/56/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Hildebrandsson (Linköping University\, Sweden)
DTSTART:20240219T150000Z
DTEND:20240219T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/57
DESCRIPTION:Title: O
ctonion algebras over schemes and the equivalence of isotopes and isometri
c forms\nby Victor Hildebrandsson (Linköping University\, Sweden) as
part of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn 2019\,
Alsaody and Gille show that\, for octonion algebras over unital commutativ
e rings\, there is an equivalence between isotopes and isometric quadratic
forms. This leads us to a question: can this equivalence be generalized t
o octonion algebras over a (not necessarily affine) scheme? We give the ba
sic definitions of octonion algebras over schemes. We show that an isotope
of an octonion algebra C over a scheme is isomorphic to a twist by an Aut
(C)–torsor. We conclude by giving an affirmative answer to our question.
\n
LOCATION:https://researchseminars.org/talk/ENAAS/57/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Gorshkov (Sobolev Institute of Mathematics\, Russia)
DTSTART:20240226T150000Z
DTEND:20240226T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/58
DESCRIPTION:Title: P
seudo-composition algebras as axial algebras\nby Ilya Gorshkov (Sobole
v Institute of Mathematics\, Russia) as part of European Non-Associative A
lgebra Seminar\n\n\nAbstract\nWe show that pseudo-composition algebras and
train algebras of rank 3 generated by idempotents are characterized as ax
ial algebras with fusion laws derived from the Peirce decompositions of id
empotents in these classes of algebras. The corresponding axial algebras a
re called PC(η)-axial algebras\, where η is an element of the ground fie
ld. As a first step towards their classification\, we describe 2− and 3-
generated subalgebras of such algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/58/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Turner (University of Birmingham\, UK)
DTSTART:20240304T150000Z
DTEND:20240304T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/59
DESCRIPTION:Title: S
kew Axial Algebras of Monster Type\nby Michael Turner (University of B
irmingham\, UK) as part of European Non-Associative Algebra Seminar\n\n\nA
bstract\nGiven a 2-generated primitive axial algebra of Monster Type\, it
has been shown that it has an axet which is regular or skew. With all the
known examples being regular\, it was proposed if any axial algebra were s
kew and if so\, can they be classified. We will begin by defining axial al
gebras and axets\, before producing examples of axial algebras with skew a
xets. We will finish by stating the complete classification of these skew
axial algebras and mention how it was proven.\n
LOCATION:https://researchseminars.org/talk/ENAAS/59/
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Alejandra Alvarez (University of Antofagasta\, Chile)
DTSTART:20240311T150000Z
DTEND:20240311T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/60
DESCRIPTION:Title: O
n S-expansions and other transformations of Lie algebras\nby María Al
ejandra Alvarez (University of Antofagasta\, Chile) as part of European No
n-Associative Algebra Seminar\n\n\nAbstract\nThe aim of this work is to st
udy the relation between S-expansions and other transformations of Lie alg
ebras. In particular\, we prove that contractions\, deformations and centr
al extensions of Lie algebras are preserved by S-expansions. We also provi
de several examples and give conditions so transformations of reduced suba
lgebras of S-expanded algebras are preserved by the S-expansion procedure.
This is a joint work with Javier Rosales-Gómez.\n
LOCATION:https://researchseminars.org/talk/ENAAS/60/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Lopes (University of Porto\, Portugal)
DTSTART:20240325T150000Z
DTEND:20240325T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/62
DESCRIPTION:Title: T
orsionfree representations of Smith algebras\nby Samuel Lopes (Univers
ity of Porto\, Portugal) as part of European Non-Associative Algebra Semin
ar\n\n\nAbstract\nWe will discuss representations of the Smith algebra whi
ch are free of finite rank over a subalgebra which plays a role analogous
to that of the (enveloping algebra of the) Cartan subalgebra of the simple
Lie algebra $\\mathfrak{sl}_2$. In the case of rank 1 we obtain a full de
scription of the isomorphism classes\, a simplicity criterion\, and a comb
inatorial algorithm to produce all composition series and the multipliciti
es of the simple factors. This is joint work with V. Futorny (SUSTech & US
P) and E. Mendonça (Lyon & USP).\n
LOCATION:https://researchseminars.org/talk/ENAAS/62/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernard Rybołowicz (Heriot-Watt University\, UK)
DTSTART:20240408T150000Z
DTEND:20240408T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/64
DESCRIPTION:Title: O
n affine nature of trusses\nby Bernard Rybołowicz (Heriot-Watt Univer
sity\, UK) as part of European Non-Associative Algebra Seminar\n\n\nAbstra
ct\nIn this presentation\, I will introduce the audience to ternary algebr
as called heaps and trusses. Specifically\, I will familiarize the audienc
e with modules over trusses\, highlighting differences with modules over r
ings. The main point will be to show the close relationship between module
s over trusses and affine spaces over rings. I will illustrate that module
s over trusses occupy a position between modules over rings and affine spa
ces over rings.\n
LOCATION:https://researchseminars.org/talk/ENAAS/64/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paola Stefanelli (University of Salento\, Italy)
DTSTART:20240415T150000Z
DTEND:20240415T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/65
DESCRIPTION:Title: P
łonka sums of set-theoretical solutions of the Yang-Baxter equation\n
by Paola Stefanelli (University of Salento\, Italy) as part of European No
n-Associative Algebra Seminar\n\n\nAbstract\nThe Płonka sum is one of the
most significant composition methods in Universal Algebra introduced by J
erzy Płonka in 1967. In particular\, Clifford semigroups have turned out
to be the first instances of Płonka sums of groups. In this talk\, we ill
ustrate a method for constructing set-theoretical solutions of the Yang-Ba
xter equation that is inspired by the notion of the Płonka sums. Moreover
\, we will show how to obtain solutions of this type by considering dual w
eak braces\, algebraic structures recently studied and described in a join
t work with Francesco Catino and Marzia Mazzotta.\n
LOCATION:https://researchseminars.org/talk/ENAAS/65/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stéphane Launois (University of Kent\, UK)
DTSTART:20240422T150000Z
DTEND:20240422T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/66
DESCRIPTION:Title: D
erivations of quantum algebras\nby Stéphane Launois (University of K
ent\, UK) as part of European Non-Associative Algebra Seminar\n\n\nAbstrac
t\nI will report on joint work in progress with Samuel Lopes and Isaac Op
pong where we aim to compute the derivations of quantum nilpotent algebras
\, a class on noncommutative algebras which includes in particular the pos
itive part of quantised enveloping algebras and quantum Schubert cells.\n
LOCATION:https://researchseminars.org/talk/ENAAS/66/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Louis Rowen (Bar-Ilan University\, Israel)
DTSTART:20240506T150000Z
DTEND:20240506T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/68
DESCRIPTION:Title: W
eakly primitive axial algebras\nby Louis Rowen (Bar-Ilan University\,
Israel) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\
nIn earlier work we studied the structure of primitive axial algebras of
Jordan type (PAJ's)\, not necessarily commutative\, in terms of their prim
itive axes. In this paper we weaken primitivity and permit several pairs o
f (left and right) eigenvalues satisfying a more general fusion rule\, bri
nging in interesting new examples such as the band semigroup algebras and
various noncommutative examples. Also we broaden our investigation to the
case of 2-generated algebras for which only one axis satisfies the fusion
rules. As an example we describe precisely the 2-dimensional axial algebra
s and the 3-dimensional and 4-dimensional weakly primitive axial algebra
s of Jordan type (weak PAJ's)\, and we see\, in contrast to the case for~P
AJ's\, that there are higher dimensional weak PAJ's generated by two axes.
We also prove a theorem that enables us to reduce weak PAJ's to uniform c
omponents.\n
LOCATION:https://researchseminars.org/talk/ENAAS/68/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pedro Fagundes (University of Campinas\, Brazil)
DTSTART:20240318T150000Z
DTEND:20240318T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/69
DESCRIPTION:Title: T
he L'vov-Kaplansky conjecture and some of its variations\nby Pedro Fag
undes (University of Campinas\, Brazil) as part of European Non-Associativ
e Algebra Seminar\n\n\nAbstract\nThe L'vov-Kaplansky conjecture claims tha
t the image of a multilinear polynomial on the full matrix algebra is a ve
ctor space. Positive results concerning the conjecture are known only for
small cases (polynomials of small degree or matrices of small size). Besid
es presenting the main results on the L'vov-Kaplasnky conjecture\, in this
talk we also will discuss some of its variations such as images of multil
inear polynomials on some subalgebras of the full matrix algebra with addi
tional structure (gradings\, involutions\, graded involutions).\n
LOCATION:https://researchseminars.org/talk/ENAAS/69/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Doikou (Heriot-Watt University\, UK)
DTSTART:20240520T150000Z
DTEND:20240520T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/70
DESCRIPTION:Title: P
arametric set-theoretic Yang-Baxter equation: p-racks\, solutions & quantu
m algebras\nby Anastasia Doikou (Heriot-Watt University\, UK) as part
of European Non-Associative Algebra Seminar\n\n\nAbstract\nThe theory of t
he parametric set-theoretic Yang-Baxter equation is established from a pur
ely algebraic point of view. We introduce generalizations of the familiar
shelves and racks named parametric (p)-shelves and racks. These objects s
atisfy a "parametric self-distributivity" condition and lead to solutions
of the Yang-Baxter equation. Novel\, non-reversible solutions are obtaine
d from p-shelve/rack solutions by a suitable parametric twist\, whereas al
l reversible set-theoretic solutions are reduced to the identity map via a
parametric twist. The universal algebras associated to both p-rack and ge
neric parametric set-theoretic solutions are next presented and the corres
ponding universal R-matrices are derived. By introducing the concept of a
parametric coproduct we prove the existence of a parametric co-associativ
ity. We show that the parametric coproduct is an algebra homomorphsim and
the universal R-matrices intertwine with the algebra coproducts.\n
LOCATION:https://researchseminars.org/talk/ENAAS/70/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rita Fioresi (University of Bologna\, Italy)
DTSTART:20240624T150000Z
DTEND:20240624T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/71
DESCRIPTION:Title: Q
uantum Principal Bundles on Quantum Projective Varieties\nby Rita Fior
esi (University of Bologna\, Italy) as part of European Non-Associative Al
gebra Seminar\n\n\nAbstract\nIn non commutative geometry\, a quantum princ
ipal bundle over an affine base is recovered through a deformation of the
algebra of its global sections: the property of being a principal bundle i
s encoded by the notion of Hopf Galois extension\, while the local trivial
ity is expressed by the cleft property. We examine the case of a projecti
ve base X in the special case X=G/P\, where G is a complex semisimple grou
p and P a parabolic subgroup. The quantization of G will then be interpret
ed as the quantum principal bundle on the quantum base space X\, obtained
via a quantum section.\n
LOCATION:https://researchseminars.org/talk/ENAAS/71/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yvain Bruned (University of Lorraine\, France)
DTSTART:20240527T150000Z
DTEND:20240527T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/72
DESCRIPTION:Title: N
ovikov algebras and multi-indices in regularity structures\nby Yvain B
runed (University of Lorraine\, France) as part of European Non-Associativ
e Algebra Seminar\n\n\nAbstract\nIn this talk\, we will present multi-Novi
kov algebras\, a generalisation of Novikov algebras with several binary op
erations indexed by a given set\, and show that the multi-indices recently
introduced in the context of singular stochastic partial differential equ
ations can be interpreted as free multi-Novikov algebras. This is parallel
to the fact that decorated rooted trees arising in the context of regular
ity structures are related to free multi-pre-Lie algebras. This is a joint
work with Vladimir Dotsenko.\n
LOCATION:https://researchseminars.org/talk/ENAAS/72/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Claudemir Fideles (University of Campinas\, Brazil)
DTSTART:20240603T150000Z
DTEND:20240603T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/73
DESCRIPTION:Title: G
raded identities in Lie algebras with Cartan gradings: an algorithm\nb
y Claudemir Fideles (University of Campinas\, Brazil) as part of European
Non-Associative Algebra Seminar\n\n\nAbstract\nThe classification of finit
e-dimensional semisimple Lie algebras in characteristic 0 represents one o
f the significant achievements in algebra during the first half of the 20t
h century. This classification was developed by Killing and by Cartan. Acc
ording to the Killing–Cartan classification\, the isomorphism classes of
simple Lie algebras over an algebraically closed field of characteristic
zero correspond one-to-one with irreducible root systems. In the infinite-
dimensional case the situation is more complicated\, and the so-called alg
ebras of Cartan type appear. It is somewhat surprising that graded identit
ies for Lie algebras have been relatively few results to that extent. In t
his presentation\, we will discuss some of the results obtained thus far a
nd introduce an algorithm capable of generating a basis for all graded ide
ntities in Lie algebras with Cartan gradings. Specifically\, over any infi
nite field\, we will apply this algorithm to establish a basis for all gra
ded identities of $U_1$\, the Lie algebra of derivations of the algebra of
Laurent polynomials $K[t\,t^{-1}]$]\, and demonstrate that they do not a
dmit any finite basis. The findings discussed in this presentation are joi
nt works with P. Koshlukov (UNICAMP).\n
LOCATION:https://researchseminars.org/talk/ENAAS/73/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erhard Neher (University of Ottawa)
DTSTART:20240610T150000Z
DTEND:20240610T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/74
DESCRIPTION:Title: C
orestriction\nby Erhard Neher (University of Ottawa) as part of Europe
an Non-Associative Algebra Seminar\n\n\nAbstract\nCorestriction is an impo
rtant technique in the theory of central-simple associative algebras over
a field. Given a finite étale extension K/F\, e.g. a Galois extension\, c
orestriction associates a central-simple associative F-algebra with every
central-simple associative K-algebra. In this talk\, I will give an introd
uction to corestriction over fields\, applicable to nonassociative algebra
s. Towards the end of my talk\, I will indicate why it is of interest to g
eneralize corestruction to schemes and sketch how this can be done (joint
work Philippe Gille and Cameron Ruether).\n
LOCATION:https://researchseminars.org/talk/ENAAS/74/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paul Laubie (University of Strasbourg)
DTSTART:20240617T150000Z
DTEND:20240617T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/75
DESCRIPTION:Title: C
ombinatorics of free pre-Lie algebras and algebras with several pre-Lie pr
oducts sharing the Lie bracket\nby Paul Laubie (University of Strasbou
rg) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nUsi
ng the theory of algebraic operads\, we give a combinatorial description o
f free pre-Lie algebras (also known as left-symmetric algebras) with roote
d trees. A numerical coincidence hints a similar description for algebras
with several pre-Lie products sharing the Lie bracket using rooted Greg tr
ees which are rooted trees with black and white vertices such that black v
ertices have at least two children. We then show that those Greg trees can
be used to give a description of the free Lie algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/75/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andronick Arutyunov (Institute of Control Sciences\, Russia)
DTSTART:20240401T150000Z
DTEND:20240401T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/76
DESCRIPTION:Title: D
erivations and other inductive operator families\nby Andronick Arutyun
ov (Institute of Control Sciences\, Russia) as part of European Non-Associ
ative Algebra Seminar\n\n\nAbstract\nDerivations on group algebras are lin
ear operators. They satisfy the Leibniz rule. Another example are Fox deri
vatives\, which satisfy a different (but very similar) identity. We will g
ive a construction which generalises all such identities and the correspon
ding operator families. The main element of such a construction is an acti
on groupoid and the space ofcharacters on it. The second step of the const
ruction are characters on special graphs (action diagrams) which are equiv
alent to classical Cayley graphs for the case of left multiplication actio
n. I will show the way to interpret inner derivations as a special case of
trivial on loops characters. And we will consider a more general ideal of
quasi-inner derivations. These results are based on the author's results\
, and the main approach was proposed in collaboration with prof. A. S. Mis
chchenko.\n
LOCATION:https://researchseminars.org/talk/ENAAS/76/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Erik Darpö (Linköping University\, Sweden)
DTSTART:20240429T150000Z
DTEND:20240429T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/77
DESCRIPTION:Title: N
on-associative algebras in an associative context\nby Erik Darpö (Lin
köping University\, Sweden) as part of European Non-Associative Algebra S
eminar\n\n\nAbstract\nFor any associative algebra A\, the left regular rep
resentation is an embedding of A into its linear endomorphism algebra End(
A). In this talk\, I shall explain how this elementary observation can be
generalised to a (less elementary) structure result for general non-associ
ative algebras. The describes the category of unital\, not necessarily ass
ociative\, algebras in terms of associative algebras with certain distingu
ished subspaces.\n
LOCATION:https://researchseminars.org/talk/ENAAS/77/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nurlan Ismailov (Astana IT University\, Kazakhstan)
DTSTART:20240701T150000Z
DTEND:20240701T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/78
DESCRIPTION:Title: O
n variety of right-symmetric algebras\nby Nurlan Ismailov (Astana IT U
niversity\, Kazakhstan) as part of European Non-Associative Algebra Semin
ar\n\n\nAbstract\nThe problem of the existence of a finite basis of identi
ties for a variety of associative algebras over a field of characteristic
zero was formulated by Specht in 1950. We say that a variety of algebras h
as the Specht property if any of its subvariety has a finite basis of iden
tities. In 1988\, A. Kemer proved that the variety of associative algebras
over a field of characteristic zero has the Specht property. Specht’s p
roblem has been studied for many well-known varieties of algebras\, such a
s Lie algebras\, alternative algebras\, right-alternative algebras\, and N
ovikov algebras. An algebra is called right-symmetric if it satisfies the
identity (a\, b\, c) = (a\, c\, b) where (a\, b\, c) = (ab)c − a(bc) is
the associator of a\, b\, c. The talk is devoted to the Specht problem for
the variety of right-symmetric algebras. It is proved that the variety of
right-symmetric algebras over an arbitrary field does not satisfy the Spe
cht property. The talk is based on the results of joint work with U. Umirb
aev.\n
LOCATION:https://researchseminars.org/talk/ENAAS/78/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrey Lazarev (Lancaster University\, UK)
DTSTART:20240715T150000Z
DTEND:20240715T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/80
DESCRIPTION:Title: C
ohomology of Lie coalgebras\nby Andrey Lazarev (Lancaster University\,
UK) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nAs
sociated to a Lie algebra g and a g-module M is a standard complex C*(g\,M
) computing the cohomology of g with coefficients in M\; this classical co
nstruction goes back to Chevalley and Eilenberg of the late 1940s. Shortly
afterwards\, it was realized that this cohomology is an example of a deri
ved functor in the category of g-modules. The Lie algebra g can be replace
d by a differential graded Lie algebra and M – with a dg g-module with
the same conclusion. Later\, a deep connection with Koszul duality was un
covered in the works of Quillen (late 1960s) and then Hinich (late 1990s).
In this talk I will discuss the cohomology of (dg) Lie coalgebras with co
efficients in dg comodules. The treatment is a lot more delicate\, undersc
oring how different Lie algebras and Lie coalgebras are (and similarly the
ir modules and comodules). A definitive answer can be obtained for so-call
ed conilpotent Lie coalgebras (though not necessarily conilpotent comodule
s). If time permits\, I will also discuss some topological applications.\n
LOCATION:https://researchseminars.org/talk/ENAAS/80/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ioannis Dokas (National and Kapodistrian University of Athens\, Gr
eece)
DTSTART:20240722T150000Z
DTEND:20240722T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/81
DESCRIPTION:Title: O
n Quillen-Barr-Beck cohomology for restricted Lie algebras\nby Ioannis
Dokas (National and Kapodistrian University of Athens\, Greece) as part o
f European Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk we
define and study Quillen-Barr-Beck cohomology for the category of restrict
ed Lie algebras. We prove that the first Quillen-Barr-Beck’s cohomology
classifies general abelian extensions of restricted Lie algebras. Moreover
\, using Duskin-Glenn’s torsors cohomology theory\, we prove a classific
ation theorem for the second Quillen-Barr-Beck cohomology group in terms o
f 2-fold extensions of restricted Lie algebras. Finally\, we give an inter
pretation of Cegarra-Aznar’s exact sequence for torsor cohomology.\n
LOCATION:https://researchseminars.org/talk/ENAAS/81/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pierre Catoire (University of the Littoral Opal Coast\, France)
DTSTART:20240812T150000Z
DTEND:20240812T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/82
DESCRIPTION:Title: T
he free tridendriform algebra\, Schroeder trees and Hopf algebras\nby
Pierre Catoire (University of the Littoral Opal Coast\, France) as part of
European Non-Associative Algebra Seminar\n\n\nAbstract\nThe notions of de
ndriform algebras\, respectively tridendriform\, describe the action of so
me elements of the symmetric groups called shuffle\, respectively quasi-sh
uffle over the set of words whose letters are elements of an alphabet\, re
spectively of a monoid. A link between dendriform and tridendriform algebr
as will be made. Those words algebras satisfy some properties but they are
not free. This means that they satisfy extra properties like commutativit
y. In this talk\, we will describe the free tridendriform algebra. It will
be described with planar trees (not necessarily binary) called Schroeder
trees. We will describe the tridendriform structure over those trees in a
non-recursive way. Then\, we will build a coproduct on this algebra that w
ill make it a (3\, 2)-dendriform bialgebra graded by the number of leaves.
Once it will be build\, we will study this Hopf algebra: duality\, quotie
nt spaces\, dimensions\, study of the primitives elements...\n
LOCATION:https://researchseminars.org/talk/ENAAS/82/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Isabel Martin-Lyons (Keele University\, UK)
DTSTART:20240902T150000Z
DTEND:20240902T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/83
DESCRIPTION:Title: S
kew Bracoids\nby Isabel Martin-Lyons (Keele University\, UK) as part o
f European Non-Associative Algebra Seminar\n\n\nAbstract\nThe skew brace w
as devised by Guanieri and Vendramin in 2017\, building on Rump's brace. S
ince then\, the skew brace has been central to the study of solutions to t
he Yang-Baxter equation\, with connections to many other areas of mathemat
ics including Hopf-Galois theory. We introduce the skew bracoid\, a genera
lisation of the skew brace which can arise as a partial quotient thereof.
We explore the connection between skew bracoids and Hopf-Galois theory\, a
s well as the more recent connection to solutions of the Yang-Baxter equat
ion.\n
LOCATION:https://researchseminars.org/talk/ENAAS/83/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tomasz Brzezinski (Swansea University\, UK)
DTSTART:20240513T150000Z
DTEND:20240513T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/84
DESCRIPTION:Title: L
ie brackets on affine spaces\nby Tomasz Brzezinski (Swansea University
\, UK) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\n
We first explore the definition of an affine space which makes no referenc
e to the underlying vector space and then formulate the notion of a Lie br
acket and hence a Lie algebra on an affine space in this framework. Since
an affine space has neither distinguished elements nor additive structure\
, the concepts of antisymmetry and Jacobi identity need to be modified. We
provide suitable modifications and illustrate them by a number of example
s. The talk is based in part on joint works with James Papworth and Krzysz
tof Radziszewski.\n
LOCATION:https://researchseminars.org/talk/ENAAS/84/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dominique Manchon (Clermont Auvergne University\, France)
DTSTART:20240909T150000Z
DTEND:20240909T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/85
DESCRIPTION:Title: P
ost-Lie algebras\, post-groups and Gavrilov's K-map\nby Dominique Manc
hon (Clermont Auvergne University\, France) as part of European Non-Associ
ative Algebra Seminar\n\n\nAbstract\nPost-Lie algebras appeared in 2007 in
algebraic combinatorics\, and independently in 2008 in the study of numer
ical schemes on homogeneous spaces. Gavrilov's K-map is a particular Hopf
algebra isomorphism\, which can be naturally described in the context of f
ree post-Lie algebras. Post-groups\, which are to post-Lie algebras what g
roups are to Lie algebras\, were defined in 2023 by C. Bai\, L. Guo\, Y. S
heng and R. Tang. Although skew-braces and braided groups are older equiva
lent notions\, their reformulation as post-groups brings crucial new infor
mation on their structure. After giving an account of the above-mentioned
structures\, I shall introduce free post-groups\, and describe a group iso
morphism which can be seen as an analogon of Gavrilov's K-map for post-gro
ups. Based on joint work with M. J. H. Al-Kaabi and K. Ebrahimi-Fard.\n
LOCATION:https://researchseminars.org/talk/ENAAS/85/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Érica Fornaroli (State University of Maringá\, Brazil)
DTSTART:20240729T150000Z
DTEND:20240729T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/86
DESCRIPTION:Title: I
nvolutions of the second kind on finitary incidence algebras\nby Éric
a Fornaroli (State University of Maringá\, Brazil) as part of European No
n-Associative Algebra Seminar\n\n\nAbstract\nLet K be a field and X a conn
ected partially ordered set. In this talk we show that the finitary incide
nce algebra FI(X\, K) of X over K has an involution of the second kind if
and only if X has an involution and K has an automorphism of order 2. We a
lso present a characterization of the involutions of the second kind on FI
(X\, K). We conclude by giving necessary and sufficient conditions for two
involutions of the second kind on FI(X\, K) to be equivalent in the case
where characteristic of K is different from 2 and every multiplicative aut
omorphism of FI(X\, K) is inner.\n
LOCATION:https://researchseminars.org/talk/ENAAS/86/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yuly Billig (Carleton University\, Canada)
DTSTART:20240819T150000Z
DTEND:20240819T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/87
DESCRIPTION:Title: Q
uasi-Poisson superalgebras\nby Yuly Billig (Carleton University\, Cana
da) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn
1985\, Novikov and Balinskii introduced what became known as Novikov algeb
ras in an attempt to construct generalizations of Witt Lie algebra. To the
ir disappointment\, Zelmanov showed that the only simple finite-dimensiona
l Novikov algebra is one-dimensional (and corresponds to Witt algebra). Th
e picture is much more interesting in the super case\, where there are man
y more generalizations of Witt algebra\, called superconformal Lie algebra
s. In 1988 Kac and Van de Leur gave a conjectural list of simple superconf
ormal Lie algebras. Their list was amended with a Cheng-Kac superalgebra\,
which was constructed several years later. However\, Novikov superalgebra
s are not flexible enough to describe all simple superconformal Lie algebr
as. In this talk\, we shall present the class of quasi-Poisson algebras. Q
uasi-Poisson algebras have two products: it is a commutative associative (
super)algebra\, a Lie (super)algebra\, and has an additional unary operati
on\, subject to certain axioms. All known simple superconformal Lie algebr
as arise from finite-dimensional simple quasi-Poisson superalgebras. In th
is talk\, we shall present basic constructions\, describe the examples of
quasi-Poisson superalgebras\, and mention some results about their represe
ntations.\n
LOCATION:https://researchseminars.org/talk/ENAAS/87/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jonas Deré (Catholic University of Leuven\, Belgium)
DTSTART:20240826T150000Z
DTEND:20240826T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/88
DESCRIPTION:Title: S
imply transitive NIL-affine actions of solvable Lie groups\nby Jonas D
eré (Catholic University of Leuven\, Belgium) as part of European Non-Ass
ociative Algebra Seminar\n\n\nAbstract\nAlthough not every 1-connected sol
vable Lie group G admits a simply transitive action via affine maps on R^n
\, it is known that such an action exists if one replaces R^n by a suitabl
e nilpotent Lie group H\, depending on G. However\, not much is known abou
t which pairs of Lie groups (G\,H) admit such an action\, where ideally yo
u only need information about the Lie algebras corresponding to G and H. I
n recent work with Marcos Origlia\, we show that every simply transitive a
ction induces a post-Lie algebra structure on the corresponding Lie algebr
as. Moreover\, if H has nilpotency class 2 we characterize the post-Lie al
gebra structures coming from such an action by giving a new definition of
completeness\, extending the known cases where G is nilpotent or H is abel
ian.\n
LOCATION:https://researchseminars.org/talk/ENAAS/88/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ana Agore (Free University of Brussels\, Belgium)
DTSTART:20241007T150000Z
DTEND:20241007T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/89
DESCRIPTION:Title: S
olutions of the set-theoretic Yang-Baxter equation of Frobenius-Separabili
ty (FS) type\nby Ana Agore (Free University of Brussels\, Belgium) as
part of European Non-Associative Algebra Seminar\n\n\nAbstract\nWe investi
gate a special class of solutions of the set-theoretic Yang-Baxter equatio
n\, called Frobenius-Separability (FS) type solutions. In particular\, we
show that the category of solutions of the set-theoretic Yang-Baxter equat
ion of Frobenius-Separability (FS) type is equivalent to the category of p
ointed Kimura semigroups. As applications\, all involutive\, idempotent\,
nondegenerate\, surjective\, finite order\, unitary or indecomposable solu
tions of FS type are classified. For instance\, if $|X| = n$\, then the nu
mber of isomorphism classes of all such solutions on $X$ that are (a) left
non-degenerate\, (b) bijective\, (c) unitary or (d) indecomposable and le
ft-nondegenerate is: (a) the Davis number $d(n)$\, (b) $\\sum_{m|n} \\\, p
(m)$\, where $p(m)$ is the Euler partition number\, (c) $\\tau(n) + \\sum_
{d|n}\\left\\lfloor \\frac d2\\right\\rfloor$\, where $\\tau(n)$ is the nu
mber of divisors of $n$\, or (d) the Harary number. The automorphism group
s of such solutions can also be recovered as automorphism groups $\\mathrm
{Aut}(f)$ of sets $X$ equipped with a single endo-function $f\\colon X\\to
X$. We describe all groups of the form $\\mathrm{Aut}(f)$ as iterations o
f direct and (possibly infinite) wreath products of cyclic or full symmetr
ic groups\, characterize the abelian ones as products of cyclic groups\, a
nd produce examples of symmetry groups of FS solutions not of the form $\\
mathrm{Aut}(f)$. Based on joint work with A. Chirvasitu and G. Militaru.\n
LOCATION:https://researchseminars.org/talk/ENAAS/89/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jörg Feldvoss (University of South Alabama\, USA)
DTSTART:20240916T150000Z
DTEND:20240916T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/90
DESCRIPTION:Title: S
emi-simple Leibniz algebras\nby Jörg Feldvoss (University of South Al
abama\, USA) as part of European Non-Associative Algebra Seminar\n\n\nAbst
ract\nLeibniz algebras were introduced by Blo(c)h in the 1960’s and redi
scovered by Loday in the 1990’s as non-anticommutative analogues of Lie
algebras. Many results for Lie algebras have been proven to hold for Leibn
iz algebras\, but there are also several results that are not true in this
more general context. In my talk\, I will investigate the structure of se
mi-simple Leibniz algebras. In particular\, I will prove a simplicity crit
erion for (left) hemi-semidirect products of a Lie algebra g and a (left)
g-module. For example\, in characteristic zero every finite-dimensional si
mple Leibniz algebra is such a hemi-semidirect product. But this also hold
s for some infinite-dimensional Leibniz algebras or sometimes in non-zero
characteristics. More generally\, the structure of finite- dimensional sem
i-simple Leibniz algebras in characteristic zero can be reduced to the wel
l-known structure of finite-dimensional semi-simple Lie algebras and their
finite-dimensional irreducible modules. If time permits\, I will apply th
ese structure results to derive some properties of finite-dimensional semi
-simple Leibniz algebras in characteristic zero and other Leibniz algebras
that are hemi-semidirect products.\n
LOCATION:https://researchseminars.org/talk/ENAAS/90/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arne Van Antwerpen (Ghent University\, Belgium)
DTSTART:20240930T150000Z
DTEND:20240930T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/91
DESCRIPTION:Title: I
ndecomposable and simple solutions of the Yang-Baxter equation\nby Arn
e Van Antwerpen (Ghent University\, Belgium) as part of European Non-Assoc
iative Algebra Seminar\n\n\nAbstract\nRecall that a set-theoretic solution
of the Yang-Baxter equation is a tuple $(X\,r)$\, where $X$ is a non-empt
y set and $r: X \\times X \\rightarrow X \\times X$ a bijective map such t
hat $$(r \\times id_X ) (id_X \\times r) (r \\times id_X) = (id_X \\times
r) (r \\times id_X ) (id_X \\times r)\,$$ where one denotes $r(x\,y)=(\\la
mbda_x(y)\, \\rho_y(x))$. Attention is often restricted to so-called non-d
egenerate solutions\, i.e. $\\lambda_x$ and $\\rho_y$ are bijective. We wi
ll call these solutions for short in the remainder of this abstract. To un
derstand more general objects\, it is an important technique to study 'min
imal' objects and glue these together. For solutions both indecomposable a
nd simple solutions fit the bill for being a minimal object. In this talk
we will report on recent work with I. Colazzo\, E. Jespers and L. Kubat on
simple solutions. In particular\, we will discuss an extension of a resul
t of M. Castelli that allows to identify whether a solution is simple\, wi
thout having to know or calculate all smaller solutions. This method emplo
ys so-called skew braces\, which were constructed to provide more examples
of solutions\, but also govern many properties of general solutions. In t
he latter part of the talk\, we discuss the extension of a method to const
ruct new indecomposable or simple solutions from old ones via cabling\, or
iginally introduced by V. Lebed\, S. Ramirez and L. Vendramin to unify the
known results on indecomposability of solutions.\n
LOCATION:https://researchseminars.org/talk/ENAAS/91/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Łukasz Kubat (University of Warsaw\, Poland)
DTSTART:20240805T150000Z
DTEND:20240805T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/92
DESCRIPTION:Title: O
n Yang-Baxter algebras\nby Łukasz Kubat (University of Warsaw\, Polan
d) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nTo e
ach solution of the Yang-Baxter equation one may associate a quadratic alg
ebra over a field\, called the YB-algebra\, encoding certain information a
bout the solution. It is known that YB-algebras of finite non-degenerate s
olutions are (two-sided) Noetherian\, PI and of finite Gelfand-Kirillov di
mension. If the solution is additionally involutive then the corresponding
YB-algebra shares many other properties with polynomial algebras in commu
ting variables (e.g.\, it is a Cohen-Macaulay domain of finite global dime
nsion). The aim of this talk is to explain the intriguing relationship bet
ween ring-theoretical and homological properties of YB-algebras and proper
ties of the corresponding solutions of the Yang-Baxter equation. The main
focus is on when such algebras are Noetherian\, (semi)prime and representa
ble. The talk is based on a joint work with I. Colazzo\, E. Jespers and A.
Van Antwerpen.\n
LOCATION:https://researchseminars.org/talk/ENAAS/92/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jorge Garcés (Technical University of Madrid\, Spain)
DTSTART:20240708T150000Z
DTEND:20240708T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/93
DESCRIPTION:Title: M
aps preserving the truncation of triple products on Cartan factors\nby
Jorge Garcés (Technical University of Madrid\, Spain) as part of Europea
n Non-Associative Algebra Seminar\n\n\nAbstract\nWe generalize the concept
of truncation of operators to JB*-triples and study some general properti
es of bijections preserving the truncation of triple products in both dir
ections between general JB*-triples. In our main result we show that a (no
n-necessarily linear nor continuous) bijection between atomic JBW*-triples
preserving the truncation of triple products in both directions (and such
that the restriction to each rank-one Cartan factor is a continuous mappi
ng) is an isometric real linear triple isomorphism.\n
LOCATION:https://researchseminars.org/talk/ENAAS/93/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilya Chevyrev (University of Edinburgh\, UK)
DTSTART:20241021T150000Z
DTEND:20241021T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/94
DESCRIPTION:Title: P
re-Lie algebras in stochastic PDEs\nby Ilya Chevyrev (University of Ed
inburgh\, UK) as part of European Non-Associative Algebra Seminar\n\n\nAbs
tract\nIn this talk\, I will discuss a general method to renormalise singu
lar stochastic partial differential equations (SPDEs) using the theory of
regularity structures. It turns out that\, to derive the renormalised equa
tion\, one can employ a convenient multi-pre-Lie algebra. The pre-Lie prod
ucts in this algebra are reminiscent of the pre-Lie product on the Grossma
n-Larson algebra of trees\, but come with several important twists. For th
e renormalisation of SPDEs\, the important feature of this multi-pre-Lie a
lgebra is that it is free in a certain sense. Based on joint work with Yva
in Bruned\, Ajay Chandra\, and Martin Hairer.\n
LOCATION:https://researchseminars.org/talk/ENAAS/94/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carla Rizzo (University of Coimbra\, Portugal)
DTSTART:20241111T150000Z
DTEND:20241111T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/95
DESCRIPTION:Title: D
ifferential identities\, almost polynomial growth and matrix algebras\
nby Carla Rizzo (University of Coimbra\, Portugal) as part of European Non
-Associative Algebra Seminar\n\n\nAbstract\nLet $F$ be a field of characte
ristic zero\, $L$ a Lie algebra over $F$\, and $A$ an $L$-algebra - that i
s\, an associative algebra over $F$ with an action of $L$ induced by deriv
ations. This action of $L$ on $A$ can be extended to an action of its univ
ersal enveloping algebra $U(L)$\, leading to the concept of $L$-identities
or differential identities of $A$: polynomials in variables $x^u := u(x)$
\, where $u \\in U(L)$\, that vanish under all substitutions of elements f
rom $A$. Differential identities were first introduced by Kharchenko in 19
78\, and\, in later years\, subsequent work by Gordienko and Kochetov has
spurred a renewed interest in both their structure and quantitative proper
ties. In this talk\, I will present recent results on the differential ide
ntities of matrix $L$-algebras\, with a particular focus on their classifi
cation and growth behavior.\n
LOCATION:https://researchseminars.org/talk/ENAAS/95/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Fernández (Technical University of Madrid\, Spain)
DTSTART:20241202T150000Z
DTEND:20241202T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/96
DESCRIPTION:Title: N
oncommutative Poisson geometry and pre-Calabi-Yau algebras\nby David F
ernández (Technical University of Madrid\, Spain) as part of European Non
-Associative Algebra Seminar\n\n\nAbstract\nIn order to define suitable no
ncommutative Poisson structures\, M. Van den Bergh introduced double Poiss
on algebras and double quasi-Poisson algebras. Furthermore\, N. Iyudu and
M. Kontsevich found an insightful correspondence between double Poisson al
gebras and pre-Calabi-Yau algebras\; certain cyclic A∞-algebras which ca
n be seen as noncommutative versions of shifted Poisson manifolds. In this
talk I will present an extension of the Iyudu-Kontsevich correspondence t
o the differential graded setting. I will also explain how double quasi-Po
isson algebras give rise to pre-Calabi-Yau algebras. This is a joint work
with E. Herscovich (EPFL).\n
LOCATION:https://researchseminars.org/talk/ENAAS/96/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicia Tocino Sánchez (University of Málaga\, Spain)
DTSTART:20241216T150000Z
DTEND:20241216T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/97
DESCRIPTION:Title: T
ensor product of evolution algebras\nby Alicia Tocino Sánchez (Univer
sity of Málaga\, Spain) as part of European Non-Associative Algebra Semin
ar\n\n\nAbstract\nThe starting point of this talk is the fact that the cla
ss of evolution algebras over a fixed field is closed under tensor product
. We prove that\, under certain conditions\, the tensor product is an evol
ution algebra if and only if every factor is an evolution algebra. Another
issue arises about the inheritance of properties from the tensor product
to the factors and conversely. For instance\, nondegeneracy\, irreducibili
ty\, perfectness and simplicity are investigated. The four-dimensional cas
e is illustrative and useful to contrast conjectures\, so we achieve a com
plete classification of four-dimensional perfect evolution algebras emergi
ng as tensor product of two-dimensional ones. We find that there are four-
dimensional evolution algebras that are the tensor product of two nonevolu
tion algebras. This is a joint work together with Yolanda Cabrera Casado\,
Dolores Martín Barquero and Cándido Martín González.\n
LOCATION:https://researchseminars.org/talk/ENAAS/97/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raschid Abedin (ETH Zürich\, Switzerland)
DTSTART:20241028T150000Z
DTEND:20241028T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/98
DESCRIPTION:Title: C
lassification of D-bialgebras via algebraic geometry\nby Raschid Abedi
n (ETH Zürich\, Switzerland) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nIn a now classic paper\, Belavin and Drinfeld categ
orized solutions to the classical Yang-Baxter equation (CYBE)\, an equatio
n crucial to the theory of integrable systems\, into three classes: ellipt
ic\, trigonometric and rational. It is possible to reproduce this result b
y geometrizing solutions of the CYBE and then applying algebro-geometric m
ethods. In this talk\, we will explain how this approach can be used to ca
tegorize Lie bialgebra structures on power series Lie algebras\, as well a
s non-associative generalizations of these structures: D-bialgebra structu
res on more general power series algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/98/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omar León Sánchez (University of Manchester\, UK)
DTSTART:20241209T150000Z
DTEND:20241209T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/99
DESCRIPTION:Title: A
basis theorem for Poisson algebras coming from infinite dimensional Lie a
lgebras\nby Omar León Sánchez (University of Manchester\, UK) as par
t of European Non-Associative Algebra Seminar\n\n\nAbstract\nI will presen
t joint work with Sue Sierra where we proved the ACC for radical Poisson i
deals of the symmetric algebra of a Dicksonian Lie algebra. Part of the ta
lk will be devoted to explaining what Dicksonian means (and give a variety
of examples)\, and then discuss the method of proof of the basis theorem.
We will observe why our result applies to graded-simple Lie algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/99/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slaven Kožić (University of Zagreb\, Croatia)
DTSTART:20241014T150000Z
DTEND:20241014T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/100
DESCRIPTION:Title:
Representations of the quantum affine vertex algebra associated with the
trigonometric $R$-matrix of type $A$\nby Slaven Kožić (University of
Zagreb\, Croatia) as part of European Non-Associative Algebra Seminar\n\n
\nAbstract\nOne important problem in the vertex algebra theory is to asso
ciate certain vertex algebra-like objects\, the quantum vertex algebras\
, to\nvarious classes of quantum groups\, such as quantum affine algebras
or double Yangians.\nIn this talk\, I will discuss this problem in th
e context of Etingof--Kazhdan's quantum affine vertex algebra $\\mathcal{V
}^c(\\mathfrak{gl}_N)$ associated with the trigonometric $R$-matrix of ty
pe $A$. \nThe main focus will be on the explicit description of the cente
r of $\\mathcal{V}^c(\\mathfrak{gl}_N)$ at the critical level $c=-N$ and\,
furthermore\, on the connection between certain classes of $\\mathcal{V}^
c(\\mathfrak{gl}_N)$-modules and representation theories of the quantum af
fine algebra of type $A$ and the orthogonal twisted $h$-Yangian. The talk
is in part based on the joint works with Alexander Molev and Lucia Bagnoli
.\n
LOCATION:https://researchseminars.org/talk/ENAAS/100/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ignacio Bajo (University of Vigo\, Spain)
DTSTART:20240923T150000Z
DTEND:20240923T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/101
DESCRIPTION:Title:
Quadratic Lie algebras admitting 2-plectic structures\nby Ignacio Bajo
(University of Vigo\, Spain) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nA 2-plectic form ω on a Lie algebra is a 3-form on
the algebra such that it is closed and non-degenerate in the sense that\,
for every nonzero x\, the bilinear form ω(x\, ·\, ·) is not identicall
y zero. We will study the existence of 2-plectic structures on the so-call
ed quadratic Lie algebras\, which are Lie algebras admitting an ad-invaria
nt pseudo-Euclidean product. It is well-known that every centerless quadra
tic Lie algebra admits a 2-plectic form but not many quadratic examples wi
th nontrivial center are known. We give several constructions to obtain la
rge families of 2-plectic quadratic Lie algebras with nontrivial center\,
many of them among the class of nilpotent Lie algebras. We give some suffi
cient conditions to assure that certain extensions of 2-plectic quadratic
Lie algebras result to be 2-plectic as well. For instance\, we show that o
scillator algebras can be naturally endowed with 2-plectic structures. We
prove that every quadratic and symplectic Lie algebra with dimension great
er than 4 also admits a 2-plectic form. Further\, conditions to assure tha
t one may find a 2-plectic which is exact on certain quadratic Lie algebra
s are obtained.\n
LOCATION:https://researchseminars.org/talk/ENAAS/101/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Fernando Montaner (University of Zaragoza\, Spain)
DTSTART:20241104T150000Z
DTEND:20241104T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/102
DESCRIPTION:Title:
Pairs of quotients of Jordan pairs\nby Fernando Montaner (University o
f Zaragoza\, Spain) as part of European Non-Associative Algebra Seminar\n\
n\nAbstract\nIn this talk we expose ongoing joint work with I Paniello on
systems of quotients (in a sense partially extending the localization theo
ry of Jordan algebras\, which in turn is inspired by the localization theo
ry of associative algebras). Localization theory in associative algebras o
riginated in the purpose of extending the construction of fields of quotie
nts of integral domains\, and therefore in the purpose of defining ring e
xtensions in which a selected set of elements become invertible. As it is
well known in associative theory that led to Goldie's theorems\, and thes
e in turn to more general localization theories for which the denominators
of the fraction-like elements of the extensions are (one-sided) ideals ta
ken in a class of filters (Gabriel filters). These ideas have been partial
ly extended to Jordan algebras by several authors (starting with Zelmanov'
s version of Goldie theory in the Jordan setting\, and its extension by Fe
rnandez López-García Rus and Montaner) and Paniello and Montaner (among
others) definition of algebras of quotients of Jordan algebras. Following
the development of Jordan theory\, a natural direction for extending these
results is considering the context of Jordan pairs. This is the objective
of the research presented here. Since obviously a Jordan pair cannot have
invertible elements unless it is an algebra\, and in this case we are bac
k in the already developed theory\, the kind of quotients that would make
a significative (proper) extension of the case of algebras should be based
in a different notion of quotient. An approach that seems to be promisin
g is considering the Jordan extension of Fountain and Gould notion of loca
l order\, as has been adapted to Jordan algebras by the work of Fernández
López\, and more recently by Montaner and Paniello with the notion of lo
cal order\, in which the bridge between algebras and pairs is established
by local algebras following the ideas of D'Amour and McCrimmon. In the tal
k this idea is exposed\, together with the state of the research\, and the
open problems that it raises.\n
LOCATION:https://researchseminars.org/talk/ENAAS/102/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos André (University of Lisboa\, Portugal)
DTSTART:20241125T150000Z
DTEND:20241125T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/103
DESCRIPTION:Title:
Supercharacters of adjoint groups of radical rings and related subgroups\nby Carlos André (University of Lisboa\, Portugal) as part of European
Non-Associative Algebra Seminar\n\n\nAbstract\nDescribing the conjugacy c
lasses and/or irreducible characters of the unitriangular group over a fin
ite field is known to be an impossibly difficult problem. Superclasses and
supercharacters have been introduced (under the names of "basic varieties
" and "basic characters") as an attempt to approximate conjugacy classes a
nd irreducible characters using a cruder version of Kirillov's method of c
oadjoint orbits.\n\nIn the past thirty years\, these notions have been rec
ognised in several areas (seemingly unrelated to representation theory): e
xponential sums in number theory\, random walks in probability and statist
ics\, association schemes in algebraic combinatorics...\n\nIn this talk\,
we will describe and illustrate the main ideas and recent developments of
the standard supercharacter theory of adjoint groups of radical rings. We
will explore the close relation to Schur rings\, and extend a well-known f
actorisation of supercharacters of unitriangular groups which explains the
alternative definition as basic characters.\n
LOCATION:https://researchseminars.org/talk/ENAAS/103/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Zadunaisky (University of Buenos Aires\, Argentina)
DTSTART:20241118T150000Z
DTEND:20241118T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/104
DESCRIPTION:Title:
Clebsch-Gordan revisited\nby Pablo Zadunaisky (University of Buenos Ai
res\, Argentina) as part of European Non-Associative Algebra Seminar\n\n\n
Abstract\nBy an ultra classical result\, the tensor product of a simple re
presentation of gl(n\,C) and its defining representation decomposes as a d
irect sum of simple representations without multiplicities. This means tha
t for each highest weight\, the space of highest weight vectors is one dim
ensional. We will give an explicit construction of these highest weight ve
ctors\, and show that they arise from the action of certain elements in th
e enveloping algebra of gl(n\,c)+gl(n\,C) on the tensor product. These ele
ments are independent of the simple representation we started with\, and i
n fact produce highest weight vectors in several other contexts. (Joint wi
th Joanna Meinel from Bonn University)\n
LOCATION:https://researchseminars.org/talk/ENAAS/104/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Stewart (University of Manchester\, UK)
DTSTART:20250106T150000Z
DTEND:20250106T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/105
DESCRIPTION:Title:
Geometric rigidity of modules for algebraic groups\nby David Stewart (
University of Manchester\, UK) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nLet k be a field\, let G be a smooth affine k-grou
p of finite type\, and V a finite-dimensional G-module. We say V is rigid
if the socle series and radical series coincide for the action of G on eac
h indecomposable summand of V\; say V is geometrically rigid (resp. absolu
tely rigid) if V is rigid after base change of G and V to an algebraic clo
sure of k (resp. any field extension of k). We show that all simple G-modu
les are geometrically rigid\, though they are not in general absolutely ri
gid. More precisely\, we show that if V is a simple G-module\, then there
is a finite purely inseparable extension k_V /k naturally attached to V su
ch that V_{k_V} is absolutely rigid as a G_{k_V} -module. The proof for co
nnected G turns on an investigation of algebras of the form K \\otimes_k E
where K and E are field extensions of k\; we give an example of such an a
lgebra which is not rigid as a module over itself. We establish the existe
nce of the purely inseparable field extension k_V /k through an analogous
version for Artinian algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/105/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Millionshchikov (Lomonosov University\, Russia)
DTSTART:20250113T150000Z
DTEND:20250113T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/106
DESCRIPTION:Title:
Narrow Lie (super)algebras\nby Dmitry Millionshchikov (Lomonosov Unive
rsity\, Russia) as part of European Non-Associative Algebra Seminar\n\n\nA
bstract\nWe discuss narrow in the sense of Shalev and Zelmanov positively
graded Lie (super)algebras. They appear in different problems of geometry\
, topology and math physics. We will pay attention to the classification r
esults as well as to the applications.\n
LOCATION:https://researchseminars.org/talk/ENAAS/106/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Mancini (University of Palermo\, Italy)
DTSTART:20250120T150000Z
DTEND:20250120T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/107
DESCRIPTION:Title:
On the representability of actions of non-associative algebras\nby Man
uel Mancini (University of Palermo\, Italy) as part of European Non-Associ
ative Algebra Seminar\n\n\nAbstract\nIt is well known that in the semi-abe
lian category Grp of groups\, split extensions\, or equivalently internal
actions\, are represented by automorphisms. This means that the category G
rp is action representable and the actor of a group X is the group Aut(X).
The notion of action representable category has proven to be quite restri
ctive: for instance\, if a non-abelian variety of non-associative algebras
\, over an infinite field of characteristic different from two\, is action
representable\, then it is the category of Lie algebras. More recently G.
Janelidze introduced the notion of weakly action representable category\,
which includes a wider class of categories. In this talk we show that for
an algebraically coherent variety of algebras and an object X of it\, it
is always possible to construct a partial algebra E(X)\, called external w
eak actor of X\, which allows us to describe internal actions on X. Moreov
er\, we show that the existence of a weak representation is connected to t
he amalgamation property\, and we give an application of the construction
of the external weak actor in the context of varieties of unitary algebras
. This is joint work with J. Brox\, (Universidad de Valladolid)\, Xabier G
arcía Martínez (Universidade de Vigo)\, Tim Van der Linden and Corentin
Vienne (Université catholique de Louvain).\n
LOCATION:https://researchseminars.org/talk/ENAAS/107/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Stasenko (HSE University\, Russia)
DTSTART:20250127T150000Z
DTEND:20250127T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/108
DESCRIPTION:Title:
Short $SL_2$-structures on simple Lie algebras and Lie's modules\nby R
oman Stasenko (HSE University\, Russia) as part of European Non-Associativ
e Algebra Seminar\n\n\nAbstract\nLet $S$ be an arbitrary reductive algebra
ic group. Let's call a homomorphism $\\Phi:S\\rightarrow\\operatorname{Au
t}(\\mathfrak{g})$ an {\\it $S$-structure on the Lie algebra $\\mathfrak{g
}$}. $S$-structures were previously invetigated by various authors\, inclu
ding E.B. Vinberg. The talk deals with $SL_2$-structures. Let's call the $
SL_2$-structure short if the representation $\\Phi$ of the group $SL_2$ de
composes into irreducible representations of dimensions 1\, 2 and 3. If we
consider irreducible representations of dimensions only 1 and 3\, we get
the well-known Tits-Kantor-Koeher construction\, which establishes a one-t
o-one correspondence between simple Jordan algebras and simple Lie algebra
s of a certain type. Similarly to the Tits–Kantor–Koeher theorem\, in
the case of short $SL_2$-structures\, there is a one-to-one correspondence
between simple Lie algebras with such a structure and the so-called simp
le symplectic Lie-Jordan structures. Let $\\mathfrak{g}$ be a Lie algebra
with $SL_2$-structure and the map $\\rho:\\mathfrak{g}\\rightarrow\\mathf
rak{gl}(U)$ be linear representation of $\\mathfrak{g}$. The homophism $\\
Psi:S\\rightarrow GL(U)$ is called a $SL_2$-structure on the Lie $\\mathfr
ak{g}$-module $U$ if $$\\Psi(s)\\rho(\\xi)u =\\rho(\\Phi(s)\\xi)\\Psi(s)u\
,\\quad\\forall s\\in S\, \\xi\\in\\mathfrak{g}\, u\\in U.$$ This construt
ion has interesting applications to the representation theory of Jordan al
gebras\, which will be discussed during the talk. We will also present a c
omplete classification of irreducible short $\\mathfrak{g}$-modules for si
mple Lie algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/108/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lina Oliveira (IST University of Lisboa\, Portugal)
DTSTART:20250203T150000Z
DTEND:20250203T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/109
DESCRIPTION:Title:
Tits–Kantor–Koecher Lie algebras and their representations\nby Lin
a Oliveira (IST University of Lisboa\, Portugal) as part of European Non-A
ssociative Algebra Seminar\n\n\nAbstract\nThis talk is an introduction to
the Tits–Kantor–Koecher Lie algebras associated with Jordan triples. I
n particular\, we will obtain representations of these algebras as matrix
Lie algebras. The necessary background will be provided\, as to render the
talk self-contained.\n
LOCATION:https://researchseminars.org/talk/ENAAS/109/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Sciandra (University of Turin\, Italy)
DTSTART:20250210T150000Z
DTEND:20250210T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/110
DESCRIPTION:Title:
Yetter—Drinfeld post-Hopf algebras and Yetter—Drinfeld relative Rota
—Baxter operators\nby Andrea Sciandra (University of Turin\, Italy)
as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nRecentl
y\, Li\, Sheng and Tang introduced post-Hopf algebras and relative Rota—
Baxter operators (on cocommutative Hopf algebras)\, providing an adjunctio
n between the respective categories under the assumption that the structur
es involved are cocommutative. We introduce Yetter— Drinfeld post-Hopf a
lgebras\, which become usual post-Hopf algebras in the cocommutative setti
ng. In analogy with the correspondence between cocommutative post-Hopf alg
ebras and cocommutative Hopf braces\, the category of Yetter—Drinfeld po
st-Hopf algebras is isomorphic to the category of Yetter—Drinfeld braces
\, introduced by the author in a joint work with D. Ferri. The latter stru
ctures are equivalent to matched pairs of actions on Hopf algebras and gen
eralise both Hopf braces and Majid’s transmutation. We also prove that t
he category of Yetter—Drinfeld post-Hopf algebras is equivalent to a sub
category of Yetter—Drinfeld relative Rota—Baxter operators (that gener
alise bijective relative Rota—Baxter operators on cocommutative Hopf alg
ebras). Once the surjectivity of the latter operators is removed\, the equ
ivalence is replaced by an adjunction and one recovers\, in the cocommutat
ive case\, the result of Li\, Sheng and Tang. The talk is partially based
on a joint work with D. Ferri.\n
LOCATION:https://researchseminars.org/talk/ENAAS/110/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guy Blachar (Bar-Ilan University\, Israel)
DTSTART:20250217T150000Z
DTEND:20250217T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/111
DESCRIPTION:Title:
Semiassociative algebras over a field\nby Guy Blachar (Bar-Ilan Univer
sity\, Israel) as part of European Non-Associative Algebra Seminar\n\n\nAb
stract\nAssociative central simple algebras are a classical subject\, rela
ted to many areas of study including Galois cohomology and algebraic geome
try. An associative central simple algebra is a form of matrices because a
maximal étale subalgebra acts on the algebra faithfully by left and righ
t multiplication. In an attempt to extract and isolate the full potential
of this point of view\, we study nonassociative algebras whose nucleus con
tains an étale subalgebra bi-acting faithfully on the algebra. We show th
at these algebras\, termed semiassociative\, are forms of a nonassociative
analogue of matrix algebras. Finally\, we consider the monoid composed of
semiassociative algebras modulo the nonassociative matrix algebras\, and
discuss its connection to the classical Brauer group. Based on joint work
with Darrell Haile\, Eliyahu Matzri\, Edan Rein and Uzi Vishne.\n
LOCATION:https://researchseminars.org/talk/ENAAS/111/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leandro Vendramin (Vrije Universiteit Brussel\, Belgium)
DTSTART:20250224T150000Z
DTEND:20250224T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/112
DESCRIPTION:Title:
Nichols Algebras over groups\nby Leandro Vendramin (Vrije Universiteit
Brussel\, Belgium) as part of European Non-Associative Algebra Seminar\n\
n\nAbstract\nNichols algebras appear in several areas of mathematics\, fro
m Hopf algebras and quantum groups to Schubert calculus and conformal fiel
d theories. In this talk\, I will review the main problems related to fini
te-dimensional Nichols algebras over groups and discuss a very recent clas
sification theorem written in collaboration with Andruskiewitsch and Hecke
nberger.\n
LOCATION:https://researchseminars.org/talk/ENAAS/112/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loïc Foissy (University of the Littoral Opal Coast\, France)
DTSTART:20250303T150000Z
DTEND:20250303T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/113
DESCRIPTION:Title:
Double bialgebra of noncrossing partitions\nby Loïc Foissy (Universit
y of the Littoral Opal Coast\, France) as part of European Non-Associative
Algebra Seminar\n\n\nAbstract\nA double bialgebra is a family $(A\,m\,\\D
elta\,\\delta)$ such that both $(A\,m\,\\Delta)$ and $(A\,m\,\\delta)$ are
bialgebras\, with the extra condition that seeing $\\delta$ as a right co
action on itself\, $m$ and $\\Delta$ are right comodules morphism over $(A
\,m\,\\delta)$. A classical example is given by the polynomial algebra $\\
mathbb{C}[X]$\, with its two classical coproducts. In this talk\, we will
present a double bialgebra structure on the symmetric algebra generated by
noncrossing partitions. The first coproduct is given by the separations o
f the blocks of the partitions\, with respect to the entanglement\, and th
e second one by fusions of blocks. This structure implies that there exist
s a unique polynomial invariant on noncrossing partitions which respects b
oth coproducts: we will give some elements on this invariant\, and applica
tions to the antipode of noncrossing partitions.\n
LOCATION:https://researchseminars.org/talk/ENAAS/113/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Fino (University of Turin\, Italy)
DTSTART:20250317T150000Z
DTEND:20250317T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/114
DESCRIPTION:Title:
Special Hermitian metrics on solvable Lie algebras\nby Anna Fino (Univ
ersity of Turin\, Italy) as part of European Non-Associative Algebra Semin
ar\n\n\nAbstract\nI will present recent results on the existence of SKT an
d balanced metrics on solvable Lie algebras. The talk is based on joint
papers with Beatrice Brienza\, Asia Mainenti and Fabio Paradiso.\n
LOCATION:https://researchseminars.org/talk/ENAAS/114/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Vallette (Sorbonne Paris North University\, France)
DTSTART:20250324T150000Z
DTEND:20250324T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/115
DESCRIPTION:Title:
Homotopy bialgebraic structures in geometry and topology\nby Bruno Val
lette (Sorbonne Paris North University\, France) as part of European Non-A
ssociative Algebra Seminar\n\n\nAbstract\nIt is well known from the PhD th
esis of Jim Stasheff that the homotopy theory of associative algebras is e
ncoded by homotopy associative algebras\, aka A_infini-algebras\, since th
is latter notion carries infini-morphisms and satisfies a homotopy transfe
r theorem\, for instance. A_infini-algebra structures encode the topologic
al data of a space on the level of cochain complexes. When one wants to en
code more data\, like the Poincaré duality of manifolds\, string topology
\, or non-commutative derived geometry\, then one has to consider further
structural operations\, like symmetric bitensors or double brackets. The p
urpose of this talk will be to present the associated new types of homotop
y bialgebras\, to explain their relationship\, and to show that they admit
suitable homotopy properties like infini-morphisms and homotopy transfer
theorem. To mention them\, we will treat pre-Calabi—Yau algebras\, homot
opy double Poisson bialgebras\, and homotopy infinitesimal balanced bialge
bras. This is based on a joint work with Johan LERAY available at arXiv:22
03.05062.\n
LOCATION:https://researchseminars.org/talk/ENAAS/115/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller (Paris Cité University\, France)
DTSTART:20250331T150000Z
DTEND:20250331T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/116
DESCRIPTION:Title:
From Coxeter-Conway friezes to cluster algebras\nby Bernhard Keller (P
aris Cité University\, France) as part of European Non-Associative Algebr
a Seminar\n\n\nAbstract\nSince their invention by Fomin-Zelevinsky in 2002
\, cluster algebras have shown up in an ever growing array of subjects in
mathematics (and in physics). In this talk\, we will approach their theory
starting from elementary examples. More precisely\, we will see how the r
emarkable integrality properties of the Coxeter-Conway friezes and the Som
os sequence find a beautiful unification and generalization in Fomin-Zelev
insky's definition of cluster variables and their Laurent phenomenon theor
em. Motivated by the periodicity of Coxeter-Conway friezes\, we will concl
ude with a general periodicity theorem\, whose proof is based on the inter
action between discrete dynamical systems and quiver representations throu
gh the combinatorial framework of cluster algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/116/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jari Desmet (Ghent University\, Belgium)
DTSTART:20250407T150000Z
DTEND:20250407T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/117
DESCRIPTION:Title:
Jordan algebras and automorphism groups of Matsuo algebras\nby Jari De
smet (Ghent University\, Belgium) as part of European Non-Associative Alge
bra Seminar\n\n\nAbstract\nPrimitive axial algebras of Jordan type half we
re introduced by Jonathan Hall\, Felix Rehren and Sergey Shpectorov in 201
5\, generalizing Jordan algebras by requiring that their idempotents satsi
fy the Peirce decomposition. More specifically\, primitive axial algebras
of Jordan type $\\frac{1}{2}$ are commutative non-associative algebras gen
erated by idempotents $a$ such that their multiplication operators $L_a$ a
re diagonalizable with eigenvalues $\\{1\,0\,\\frac{1}{2}\\}$\, such that
the fusion laws $V_1 = \\langle a\\rangle$\, $V_0^2 \\subseteq V_0$\, $V_0
V_{\\frac{1}{2}} \\subseteq V_{\\frac{1}{2}}$ and $V_{\\frac{1}{2}}^2 \\su
bseteq V_0 \\oplus V_1$ hold\, where $V_\\lambda$ is the $\\lambda$-eigens
pace of $L_a$. The most well-known examples of this class of algebras are
either Jordan algebras or Matsuo algebras\, certain non-assocative algebra
s related to 3-transposition groups that Atsushi Matsuo discovered while s
tudyin vertex operator algebras. In this talk\, we will sketch how one can
distinguish these two classes in terms of their automorphism groups. In p
articular\, primitive axial algebras of Jordan type half with large automo
rphism groups are automatically Jordan while the automorphism groups of no
n-Jordan Matsuo algebras are usually finite\, with one infinite family of
exceptions.\n
LOCATION:https://researchseminars.org/talk/ENAAS/117/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Blecher (University of Houston\, USA)
DTSTART:20250310T150000Z
DTEND:20250310T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/118
DESCRIPTION:Title:
Jordan operator algebras and beyond\nby David Blecher (University of H
ouston\, USA) as part of European Non-Associative Algebra Seminar\n\n\nAbs
tract\nWe discuss the class of Jordan operator algebras\, including report
ing on recent progress on their M-ideals (joint with M. Neal\, A. Peralta
\, S. Su). More generally we consider some nonassociative algebras motiv
ated by Hilbert space operator algebraic theory and group representations.
\n
LOCATION:https://researchseminars.org/talk/ENAAS/118/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giovanna Carnovale (University of Padua\, Italy)
DTSTART:20250414T150000Z
DTEND:20250414T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/119
DESCRIPTION:Title:
Nichols algebras over simple groups\nby Giovanna Carnovale (University
of Padua\, Italy) as part of European Non-Associative Algebra Seminar\n\n
\nAbstract\nNichols (small shuffle) algebras are a family of graded algebr
as including the symmetric algebras\, the exterior algebras\, the positive
part of quantized enveloping algebras. They are defined by generators an
d relations that depend on a vector space V and a solution of the braid eq
uation on V\\otimes V. A subclass of them\, which is relevant for the clas
sification program of finite-dimensional Hopf algebras developed by Andrus
kiewitsch and Schneider\, consists of those for which the solution of the
braid equation stems from a suitable graded representation of a finite gro
up G. A folklore conjecture states that there are no non-trivial finite-di
mensional Nichols algebras in this family if G is a non-abelian simple gro
up. I will report on progress on this conjecture\, based on a collaboratio
ns with N. Andruskiewitsch\, G. García and M. Costantini.\n
LOCATION:https://researchseminars.org/talk/ENAAS/119/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Kotchetov (Memorial University\, Canada)
DTSTART:20250421T150000Z
DTEND:20250421T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/120
DESCRIPTION:Title:
Almost fine gradings on algebras and classification of gradings up to isom
orphism\nby Mikhail Kotchetov (Memorial University\, Canada) as part o
f European Non-Associative Algebra Seminar\n\n\nAbstract\nSince the works
of Patera-Zassenhaus (1989) and Bahturin-Sehgal-Zaicev (2001)\, the proble
m of classifying gradings by groups on various algebras has received much
attention. There are typically two kinds of classification of gradings on
a given algebra A: fine gradings up to equivalence or all G-gradings\, for
a fixed group G\, up to isomorphism. These classifications are related\,
but it is not straightforward to pass from one to the other. In this talk\
, based on a recent paper with A. Elduque\, we introduce a class of gradin
gs\, which we call almost fine\, on a finite-dimensional algebra A over an
algebraically closed field\, such that every G-grading on A is obtained f
rom an almost fine grading in an essentially unique way (which is not the
case with fine gradings). For abelian groups\, we give a method of obtaini
ng all almost fine gradings if fine gradings are known. If time permits\,
we will illustrate this approach in the case of simple Lie algebras in cha
racteristic 0: to any abelian group grading with nonzero identity componen
t\, we attach a (possibly nonreduced) root system Φ and construct an adap
ted Φ-grading.\n
LOCATION:https://researchseminars.org/talk/ENAAS/120/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mikhail Ignatyev (HSE University\, Russia)
DTSTART:20250428T150000Z
DTEND:20250428T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/121
DESCRIPTION:Title:
Tangent cones to Schubert varieties form Kac--Moody groups\nby Mikhail
Ignatyev (HSE University\, Russia) as part of European Non-Associative Al
gebra Seminar\n\n\nAbstract\nStudying of the geometry of Schubert varietie
s for simple algebraic finite-dimensional complex groups is a classical to
pic in algebraic geometry. Tangent cones encode a lot of geometric informa
tion about singularity of Schubert varieties. One of the very important to
ol in investigation properties of tangent cones are Kostant--Kumar polynom
ials. I will discuss how this topics can be generalized to the case of Kac
--Moody groups.\n
LOCATION:https://researchseminars.org/talk/ENAAS/121/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geoffrey Janssens (Catholic University of Louvain\, Belgium)
DTSTART:20250505T150000Z
DTEND:20250505T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/122
DESCRIPTION:Title:
On the loop Hecke algebra\nby Geoffrey Janssens (Catholic University o
f Louvain\, Belgium) as part of European Non-Associative Algebra Seminar\n
\n\nAbstract\nTo any braid group $B_n$ there is an associated (Iwahori
-)Hecke algebra $H_q (n)$. Over time this algebra has shown to be as i
ntriguing as $B_n$. For example\, $H_q (n)$ possesses a representation
for which it is in a Schur–Weyl relation with $U_q (sl_d). One poss
ible interpretation of classical braid groups is as a fundamental group of
the space of configurations of $n$ distinct points in $R^2$. Taking this
motion group perspective\, it is natural to consider configurations of $n
$ unit circles $S^1$. This yields the so-called Loop Braid group. Damiani
–Martin–Rowell associated an analogue of the Hecke algebra and made a
conjecture on the dimension of this Loop Hecke algebra. In this talk we wi
ll firstly briefly introduce the mentioned objects and subsequently tell a
bout how the above Schur–Weyl picture adapts to the Loop setting. In the
last part of the talk we will discuss the simple representations and the
Jacobson radical.\n
LOCATION:https://researchseminars.org/talk/ENAAS/122/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sue Sierra (University of Edinburgh\, UK)
DTSTART:20250519T150000Z
DTEND:20250519T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/123
DESCRIPTION:Title:
Ideals of enveloping algebras of loop algebras\nby Sue Sierra (Univers
ity of Edinburgh\, UK) as part of European Non-Associative Algebra Seminar
\n\n\nAbstract\nLet g be a finite-dimensional simple Lie algebra\, and con
sider the loop algebra $L_g = g[t\, t^{-1}]$ and the affine Lie algebra $\
\hat{g}$\, which is an extension of $L_g$ by a central element $c$. We inv
estigate two-sided ideals in the universal enveloping algebra $U(L_g)$. I
t is known that the rings $U(\\hat{g})/(c-\\lambda)$ are simple for any no
nzero scalar $\\lambda$\, but the two-sided structure of $U(L_g) = U(\\hat
{g}/(c))$ is more complicated. We show that $U(L_g)$ does not satisfy the
ascending chain condition on two-sided ideals\, but that the two-sided id
eals still have a nice structure: there is a canonical collection of ideal
s $I_n$\, parameterised by positive integers\, so that any two-sided ideal
of $U(L_g)$ contains some $I_n$. The ideals $I_n$ can be thought of as u
niversal annihilators of classes of finite-dimensional representations of
$L_g$. This is a preliminary report on joint work with Alexey Petukhov.\n
LOCATION:https://researchseminars.org/talk/ENAAS/123/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Charles Young (University of Hertfordshire\, UK)
DTSTART:20250512T150000Z
DTEND:20250512T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/124
DESCRIPTION:Title:
Higher current algebras and chiral algebras\nby Charles Young (Univers
ity of Hertfordshire\, UK) as part of European Non-Associative Algebra Sem
inar\n\n\nAbstract\nVertex algebras capture physicists' notion of OPEs in
chiral CFTs\, in complex dimension one. For various motivations\, one woul
d like to have analogs of vertex algebras in higher dimensions. Chiral alg
ebras\, in the sense of Beilinson-Drinfeld and Francis-Gaitsgory\, provide
a promising framework here\, because they re-express the vertex algebra a
xioms (which are rather sui generis\, and therefore hard to generalize) as
something more recognizable (a chiral algebra is a Lie algebra\, of a sor
t).\n\nI will review this\, and then go on to introduce a certain concrete
model of the unit chiral algebra in higher complex dimensions. We shall s
ee that in going to higher dimensions\, one naturally moves from Lie algeb
ras to their homotopy analogs\, L-infinity algebras\, and from chiral alge
bras to homotopy chiral algebras in a sense recently introduced by Malikov
-Schechtman. The main tool in the talk will be a new model -- the polysimp
licial model -- of derived sections of the sheaf of functions on higher co
nfiguration spaces. The hope is that this model will prove well-adapted to
doing concrete calculations.\n\nThis is joint work in preparation with Zh
engping Gui and Laura Felder.\n
LOCATION:https://researchseminars.org/talk/ENAAS/124/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Farinati (University of Buenos Aires\, Argentina)
DTSTART:20250602T150000Z
DTEND:20250602T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/125
DESCRIPTION:Title:
The Tits construction for SHORT $\\mathfrak{sl}_2$-super-structures.\n
by Marco Farinati (University of Buenos Aires\, Argentina) as part of Euro
pean Non-Associative Algebra Seminar\n\n\nAbstract\nWhen we have an action
of $\\mathfrak{sl}_2$ on a given structure\, one may decompose it on its
isotypic components. More concretely\, if $A$ is a finite dimensional "alg
ebra" with an operation $m:A\\otimes A\\to A$\, one may decompose $A=\\opl
us_n V_n\\otimes M_n$\, where $V_n$ is the irreducible $\\mathfrak{sl}_2$-
module of highest weight $n$ (and dimension $n+1$) and $M_n$ is just a "mu
ltiplicity" vector space. If the operation $m$ is $\\mathfrak{sl}_2$-linea
r\, then\, a priori\, several restrictions for the operation $m$ can be d
educed\, and algebraic identities (e.g. associativity\, Jacobi identity\,
symmetry\, antisymmetry\,...) of $A$ can be translated into operations and
identities on the $M_n$'s.\n\nIn case the only isotypical components that
appear are the trivial ($V_0$) and the adjoint ($V_2$)\, then the $\\math
frak{sl}_2$ structure is called VERY SHORT. In case the only isotypical co
mponents that appear are the trivial ($V_0$)\, the adjoint ($V_2$)\, and t
he defining 2-dimensional representation ($V=\\mathcal{C}^2=V_1$) then the
$\\mathfrak{sl}_2$ structure is called SHORT.\n\nThe case of VERY SHORT $
\\mathfrak{sl}_2$ Lie algebras is a classical object studied by Tits and l
eads to Jordan algebras. There is also a kind of reciprocal knowledge like
TKK-construction (TKK from Tits-Kantor-Koecher): given a Jordan algebra o
ne can assign to it a natural (but not functorial) Lie algebra. The functo
riality problem was solved by Alison and Gao\, we call it the TAG construc
tion.\n\nWhen the natural representation $V$ also appears\, Elduque et al.
made the "translation" from Lie axioms into an object called "Jordan trip
le".\n\nIf the algebra is a SUPER Lie algebra\, but VERY SHORT\, then both
TKK and TAG constructions were generalized to the super case by Barbier a
nd Shang.\n\nIn this talk\, I will show that TKK and TAG constructions can
be extended to the SHORT super case. That is\, one can make a constructio
n beginning from a Jordan super triple (not just a Jordan algebra) and get
a Lie super algebra. In case the Jordan triple is a usual one\, we get a
reciprocal construction to Elduque's one. In case the Jordan triple is jus
t a Jordan algebra\, but super\, we generalize Shang's work for super Jord
an algebras. On the way of doing that\, adapting to the short case an intr
insic description of Shang of the Jordan algebra associated to a very shor
t Lie algebra\, we discover two different possible ternary Jordan structur
e on the "Jordan data" associated to a short Lie algebra: one was consider
ed previously by Elduque et al (in the non super case) and the other can b
e described in a simpler way using the Lie-intrinsic description\, and it
happens that this second one is more suitable for the functorial generaliz
ation of TKK and TAG construction for short (and super) construction.\n
LOCATION:https://researchseminars.org/talk/ENAAS/125/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikita Safonkin (Leipzig University\, Germany)
DTSTART:20250609T150000Z
DTEND:20250609T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/126
DESCRIPTION:Title:
What is a double star-product?\nby Nikita Safonkin (Leipzig University
\, Germany) as part of European Non-Associative Algebra Seminar\n\n\nAbstr
act\nDouble Poisson brackets\, introduced by M. Van den Bergh in 2004\, ar
e noncommutative analogs of the usual Poisson brackets in the sense of the
Kontsevich-Rosenberg principle: they induce Poisson structures on the spa
ce of N-dimensional representations of an associative algebra A for any N
. The problem of deformation quantization of double Poisson brackets was r
aised by D. Calaque in 2010\, and had remained open since then. In the tal
k\, I plan to present a possible answer to the question in the title. Name
ly\, I will discuss a structure on an associative algebra A that induces a
star-product under the representation functor and\, therefore\, according
to the Kontsevich-Rosenberg principle\, can be viewed as an analog of sta
r-products in noncommutative geometry. If time permits\, I will also discu
ss a way to invert the Kontsevich-Rosenberg principle by introducing the n
otion of a double algebra over an arbitrary operad. The talk is based on a
rXiv:2506.00699.\n
LOCATION:https://researchseminars.org/talk/ENAAS/126/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Brais Ramos Pérez (University of Santiago de Compostela\, Spain)
DTSTART:20250616T150000Z
DTEND:20250616T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/127
DESCRIPTION:Title:
Twisted relative Rota-Baxter operators and their relation with Hopf trusse
s\nby Brais Ramos Pérez (University of Santiago de Compostela\, Spain
) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn th
is talk we are going to introduce the category of twisted relative Rota-Ba
xter operators in a braided monoidal setting together with a procedure for
constructing examples of such structures based on idempotent Hopf algebra
morphisms\, and also we are going to prove that\, under certain condition
s\, the following results hold: There exists an adjoint pair of functors b
etween the category of Hopf trusses and the category of twisted relative R
ota-Baxter operators. The previous adjunction induces a categorical equiva
lence between the category of Hopf trusses and the subcategory of invertib
le twisted relative Rota-Baxter operators.\n
LOCATION:https://researchseminars.org/talk/ENAAS/127/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agata Pilitowska (Warsaw University of Technology\, Poland)
DTSTART:20250623T150000Z
DTEND:20250623T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/128
DESCRIPTION:Title:
Diagonals of solutions of the Yang-Baxter equation\nby Agata Pilitowsk
a (Warsaw University of Technology\, Poland) as part of European Non-Assoc
iative Algebra Seminar\n\n\nAbstract\nThe Yang--Baxter equation is one of
the fundamental equations occurring in statistical mechanics and quantum f
ield theory. I will show that the diagonal mappings are bijections in any
non-degenerate set-theoretical solution. This immediately gives that any n
on-degenerate solution is bijective and affirmatively answers question sta
ted by Cedo\, Jespers and Verwimp. I also prove that\, for a subclass of s
olutions called permutational\, one-sided non-degeneracy is sufficent for
the diagonal to be invertible. This is joint work with Premysl Jedlicka (C
zech University of Life Sciences).\n
LOCATION:https://researchseminars.org/talk/ENAAS/128/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vincenzo Nardozza (University of Bari Aldo Moro\, Italy)
DTSTART:20250630T150000Z
DTEND:20250630T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/129
DESCRIPTION:Title:
The Grassmann algebra: identities\, derivations\, and differential identit
ies\nby Vincenzo Nardozza (University of Bari Aldo Moro\, Italy) as pa
rt of European Non-Associative Algebra Seminar\n\n\nAbstract\nStarting fro
m Kemer's work\, the Grassmann algebra of an infinite-dimensional vector s
pace played a key role in classical PI-Theory. Still\, there are new branc
hes of PI-Theory\, involving PI-algebras with additional structures\, wher
e the Grassmann algebra either is a key ingredient as well\, or leads to i
nteresting identities. In particular\, the differential identities of the
Grassmann algebra under some derivation action will be presented\n
LOCATION:https://researchseminars.org/talk/ENAAS/129/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tuan Pham (University of Edinburgh\, UK)
DTSTART:20250707T150000Z
DTEND:20250707T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/130
DESCRIPTION:Title:
The orbit method for the Virasoro algebra\nby Tuan Pham (University of
Edinburgh\, UK) as part of European Non-Associative Algebra Seminar\n\n\n
Abstract\nThe orbit method is a fundamental tool to study a finite dimensi
onal solvable Lie algebra g. It relates the annihilators of irreducible re
presentation of \\g to the coadjoint orbits of g* . In my talk\, I will ex
tend this story to the Witt and Virasoro algebra infinite dimensional Lie
algebras which are important in physics and representation theory. I will
construct an induced module from an element of Vir* and show that its anni
hilator is a primitive ideal. I will also construct an algebra homomorphis
m that allows one to relate the orbit method for Vir to that of a finite d
imensional solvable Lie algebra.\n
LOCATION:https://researchseminars.org/talk/ENAAS/130/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elkin Quintero Vanegas (Federal University of Amazonas\, Brazil)
DTSTART:20250714T150000Z
DTEND:20250714T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/131
DESCRIPTION:Title:
Albert's Problem and its connections\nby Elkin Quintero Vanegas (Feder
al University of Amazonas\, Brazil) as part of European Non-Associative Al
gebra Seminar\n\n\nAbstract\nIn this talk\, we abord the question of exist
ence of simple nilalgebras within the class of commutative power associati
ve algebras. We give some equivalences that related the existence of such
algebras to the non degenerated bilinear forms or faithful irreducible mo
dules.\n
LOCATION:https://researchseminars.org/talk/ENAAS/131/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sebastiano Argenti (University of Basilicata\, Italy)
DTSTART:20250721T150000Z
DTEND:20250721T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/132
DESCRIPTION:Title:
Gradings on simple Lie superalgebras\nby Sebastiano Argenti (Universit
y of Basilicata\, Italy) as part of European Non-Associative Algebra Semin
ar\n\n\nAbstract\nIn this talk\, we briefly discuss the recent development
s regarding the classification of gradings on simple Lie superalgebras. Th
e interest on Lie superalgebras stems from theoretical physics while the s
tudy of their algebraic properties was fostered by Kac and his classificat
ion of the simple finite dimensional Lie superalgebras. The classification
of the gradings on such algebras is an ongoing work collecting the effort
s of many people. We will give an overview of the progress in this directi
on and then we will focus on the case of exceptional simple Lie superalgeb
ras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/132/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sachin Sharma (Indian Institute of Technology Kanpur\, India)
DTSTART:20250818T150000Z
DTEND:20250818T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/133
DESCRIPTION:Title:
Representation of map extended Witt algebras\nby Sachin Sharma (Indian
Institute of Technology Kanpur\, India) as part of European Non-Associati
ve Algebra Seminar\n\n\nAbstract\nIn this talk\, I will speak on the class
ification result of irreducible modules for map extended Witt algebras wit
h finite-dimensional weight spaces. They turn out to be either modules wit
h uniformly bounded weight spaces or highest-weight modules. We further pr
ove that all these modules are single point evaluation modules (n ≥ 2).
So they are actually irreducible modules for extended Witt algebras. This
is a joint work with S. Eswara Rao\, Priyanshu Chakraborty\, and Ritesh Ku
mar Pandey.\n
LOCATION:https://researchseminars.org/talk/ENAAS/133/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Johan Richter (Blekinge Institute of Technology\, Sweden)
DTSTART:20250825T150000Z
DTEND:20250825T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/134
DESCRIPTION:Title:
Non-associative versions of Hilbert’s basis theorem\nby Johan Richte
r (Blekinge Institute of Technology\, Sweden) as part of European Non-Asso
ciative Algebra Seminar\n\n\nAbstract\nI will describe several non-associa
tive versions of Hilbert’s basis theorem\, for non-associative Ore exten
sions and related structures. An interesting asymmetry between the left an
d right versions of Hilbert’s basis theorem will appear\, not present in
the associative case. The talk is based on joint work with Per Bäck.\n
LOCATION:https://researchseminars.org/talk/ENAAS/134/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Irene Paniello (University of Zaragoza\, Spain)
DTSTART:20250901T150000Z
DTEND:20250901T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/135
DESCRIPTION:Title:
Local inheritance in Jordan algebras of quotients\nby Irene Paniello (
University of Zaragoza\, Spain) as part of European Non-Associative Algebr
a Seminar\n\n\nAbstract\nSince their introduction by K. Meyberg in the non
associative setting\, local algebras have played a key role in the study o
f Jordan systems. The local inheritance of regularity conditions (such as
nondegenerancy\, strong primeness or primitivity) is a well-known result
that undoubtedly contributed to the development of the structure theory
\, not only of Jordan algebras\, but also of Jordan pairs and triple syste
ms. \n\nA rather usual strategy to tackle many Jordan questions is to d
ifferentiate Jordan systems depending on whether their\n local algebras
satisfy or not certain properties. For instance\, some of the recent r
esults on localization theory for Jordan algebras have been established t
aking advantage of the \n dichotomy between Jordan algebras having\, or
not\, local algebras satisfying polynomial identities.\nAnalogously\,
the formulation of Goldie local theory for Jordan algebras is closely re
lated to Jordan algebras \nadmitting Lesieur-Croisot local algebras.\n \
n \n The above considerations lead us to consider\, in the Jordan algebra
setting\, how local algebras of Jordan algebras interact with their algeb
ras of quotients (in Utumi's sense). This problem is motivated by a prev
ious question originally posed\, in the associative setting for (maximal
\, Martindale and symmetric) rings of quotients of semiprime rings by G\\'
omez Lozano and Siles Molina\, who proved that both constructions commute
whenever the element at which the local algebra is defined becomes von Neu
mann regular in the corresponding ring of quotients. \n \n In this talk
we will display the Jordan algebra case of this problem\, proving that\,
for any nondegenerate Jordan algebra\, whenever the element defining the
local algebra becomes von Neumann regular in its maximal algebra of quot
ients\, taking local algebras and maximal algebras of quotients are comm
uting constructions.\n \n \nThis is a joint work with Fernando Montaner (U
niversity of Zaragoza).\n
LOCATION:https://researchseminars.org/talk/ENAAS/135/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dijana Ilišević (University of Zagreb\, Croatia)
DTSTART:20251006T150000Z
DTEND:20251006T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/136
DESCRIPTION:Title:
Spectral properties of isometries of JB*-triples and C*-algebras\nby D
ijana Ilišević (University of Zagreb\, Croatia) as part of European Non-
Associative Algebra Seminar\n\n\nAbstract\nA JB*-triple is a complex Banac
h space with a continuous non-associative triple product that satisfies sp
ecific axioms. Any C*-algebra can be seen as a JB*-triple with respect to
the triple product defined using the algebra product and the involution. S
urjective linear isometries of JB*-triples are closely related to the corr
esponding algebraic isomorphisms. The aim of this talk is to recall and co
nnect some recent and not so recent results on the structure of surjective
isometries of JB*-triples\, specifically C*-algebras\, following a long l
ine of work starting with the celebrated Banach-Stone theorem. Attention w
ill be focused on periodic isometries\, their eigenprojections and eigenva
lues. They will be studied in connection with the following inverse eigenv
alue problem for isometries: when is a given finite set of modulus one com
plex numbers spectrum of a surjective linear isometry? The necessary condi
tions on such a set will be presented.\n
LOCATION:https://researchseminars.org/talk/ENAAS/136/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Simone Blumer (University of Vienna\, Austria)
DTSTART:20250526T150000Z
DTEND:20250526T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/137
DESCRIPTION:Title:
Quadratically defined Lie algebras and HNN-extension\nby Simone Blumer
(University of Vienna\, Austria) as part of European Non-Associative Alge
bra Seminar\n\n\nAbstract\nIn this talk\, we will delve into the class of
Lie algebras defined by quadratic relations\, focusing on the explicit com
putation of their cohomology rings in specific cases. These algebras natur
ally arise in the broader context of positively graded Lie algebras\, wher
e they play a significant structural role. The theory of HNN-extensions pl
ays a crucial role in this context\, providing a powerful tool for decompo
sing quadratic Lie algebras into smaller components. Moreover\, we will ex
plore how HNN-extensions can be used to embed finitely presented positivel
y graded Lie algebras into quadratic ones.\n
LOCATION:https://researchseminars.org/talk/ENAAS/137/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zohreh Ravanpak (West University of Timisoara\, Romania)
DTSTART:20250728T150000Z
DTEND:20250728T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/138
DESCRIPTION:Title:
NL Bialgebras: Structures\, Hierarchies\, and Applications in Integrable S
ystems\nby Zohreh Ravanpak (West University of Timisoara\, Romania) as
part of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn this t
alk\, I will introduce the concept of NL bialgebras\, an algebraic structu
re that combines a Lie bialgebra with a Nijenhuis operator on a Lie algebr
a. The compatibility between these two structures leads to a rich framewor
k for studying deformations and hierarchies of Lie bialgebras. As an impor
tant application\, I will show how the underlying algebraic framework of t
he Euler-top system can be represented as a weak NL bialgebra\, highlighti
ng the significance of these structures in the context of integrable syste
ms.\n
LOCATION:https://researchseminars.org/talk/ENAAS/138/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alan Guimarães (Federal University of Rio Grande do Norte\, Brazi
l)
DTSTART:20250804T150000Z
DTEND:20250804T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/139
DESCRIPTION:Title:
A characterization of the natural grading of the Grassmann algebra\nby
Alan Guimarães (Federal University of Rio Grande do Norte\, Brazil) as p
art of European Non-Associative Algebra Seminar\n\n\nAbstract\nLet E be th
e infinite-dimensional Grassmann algebra over a field of characteristic di
fferent from 2. In this talk\, we investigate the Isomorphism Problem in t
he context of the natural Z2-grading of E. We show that this grading is co
mpletely determined by its graded polynomial identities. Additionally\, we
explore the connection between Z2-gradings on E and its automorphisms of
order two.\n
LOCATION:https://researchseminars.org/talk/ENAAS/139/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Paolo Saracco (University of Seville\, Spain)
DTSTART:20250915T150000Z
DTEND:20250915T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/140
DESCRIPTION:Title:
Integrals for bialgebras\nby Paolo Saracco (University of Seville\, Sp
ain) as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nAn
extremely familiar notion in Hopf algebra theory is that of an \\emph{int
egral}. If $G$ is a compact topological group\, then a Haar integral on $G
$ is a linear functional $\\mathcal{C}(G) \\to \\mathbb{R}$ which is trans
lation invariant.\n%\nA well-known result by Larson and Sweedler shows tha
t integrals on a Hopf algebra can be obtained by applying the Structure Th
eorem of Hopf modules to the rational part of its linear dual\, i.e.\, the
space of integrals comes from a right adjoint functor from a category of
modules to the category of vector spaces. \n%\nIn this seminar we will dis
cuss how this construction can be carried out even in the absence of an an
tipode\, offering a novel perspective on integrals which differs profoundl
y from their classical description as ``colinear forms''. Our approach lea
ds to a new notion of integrals for bialgebras which does not require\, an
d does not imply\, the existence of an antipode.\n\nTime permitting\, we w
ill seize this opportunity to say a few words about Hopf envelopes of bial
gebras\, since in many cases of interest integrals for a bialgebra are in
bijection with integrals for its Hopf envelope.\n%\nThe Hopf envelope of a
bialgebra B is a certain universal Hopf algebra that we can associate wit
h B and that plays for it the same role that the universal enveloping grou
p plays for a monoid. \n%In categorical terms\, the Hopf envelope is the l
eft adjoint to the forgetful functor from Hopf algebras to bialgebras\, he
nce it may be legitimately called the free Hopf algebra generated by B. \n
Its existence is a well-known fact in Hopf algebra theory\, but its constr
uction is very technical. Nevertheless\, there are a number of cases where
we can realize the Hopf envelope of a bialgebra B as a suitable quotient
of B itself and we can take advantage of it to study integrals for the cor
responding bialgebra.\n\n\\medskip\n\n\\centering \nThis talk is based on
an ongoing project with A.\\ Ardizzoni and C.\\ Menini.\n
LOCATION:https://researchseminars.org/talk/ENAAS/140/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alessio Marrani (University of Hertfordshire\, UK)
DTSTART:20250922T150000Z
DTEND:20250922T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/141
DESCRIPTION:Title:
Okubo Algebra: a new approach to Quantum Chromodynamics?\nby Alessio M
arrani (University of Hertfordshire\, UK) as part of European Non-Associat
ive Algebra Seminar\n\n\nAbstract\nThis talk discusses the possible releva
nce of the Okubonions (i.e. the real Okubo algebra) in quantum chromodynam
ics (QCD). We start and present the Okubonions within the 8-dimensional re
al division composition algebras\, and then discuss their realization as t
he traceless cubic simple Jordan algebra over the complex numbers\, endowe
d with a suitable deformation of the Michel-Radicati product. The Okubonio
ns lack a unit element and exhibit the unique feature of sitting in the ad
joint representation of their automorphism group SU(3)\; in this respect\,
they are fundamentally different from the better-known Octonions. While t
hese latter may represent quarks (and singlets of the QCD SU(3) color gaug
e group)\, the Okubonions are conjectured to represent the gluons\, i.e. t
he gauge bosons of the colour group. However\, it is remarked that the SU(
3) groups pertaining to Okubonions and Octonions are distinct and inequiva
lent subgroups of Spin(8) that share no common SU(2) subgroup. Main refere
nce : arXiv:2309.17435 [hep-th]\n
LOCATION:https://researchseminars.org/talk/ENAAS/141/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abror Khudoyberdiyev (Institute of Mathematics\, Uzbekistan)
DTSTART:20250811T150000Z
DTEND:20250811T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/142
DESCRIPTION:Title:
Transposed Poisson structures and quasi-derivations\nby Abror Khudoybe
rdiyev (Institute of Mathematics\, Uzbekistan) as part of European Non-Ass
ociative Algebra Seminar\n\n\nAbstract\nIn this talk\, we describe transpo
sed Poisson structures on Witt and Virasoro-type algebras. We compute 1/2-
derivations on the deformative Schrodinger-Witt algebra\, not-finitely gra
ded Witt algebras\, and not-finitely graded Heisenberg-Witt algebras. We c
lassify all transposed Poisson structures on such algebras\, as well as de
formed generalized Heisenberg-Virasoro and not-finitely graded Heisenberg-
Virasoro algebras. Furthermore\, we compute the quasi-derivations of the W
itt and Virasoro algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/142/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nishant Rathee (IISER Mohali\, India)
DTSTART:20250929T150000Z
DTEND:20250929T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/143
DESCRIPTION:Title:
Extensions of Skew Braces\nby Nishant Rathee (IISER Mohali\, India) as
part of European Non-Associative Algebra Seminar\n\n\nAbstract\nSkew brac
es are important algebraic structures arising from non-degenerate set-theo
retic solutions of the Yang–Baxter equation. In this talk\, we discuss e
xtensions of skew braces and their connection with the second cohomology g
roup. We will also see how an action of a skew brace on an abelian group n
aturally induces a representation of the skew brace. Furthermore\, we expl
ore split extensions of skew braces and their relation to the splitting of
group extensions.\n
LOCATION:https://researchseminars.org/talk/ENAAS/143/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ilja Gogić (University of Zagreb\, Croatia)
DTSTART:20251013T150000Z
DTEND:20251013T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/144
DESCRIPTION:Title:
Spectrum-shrinking maps and nonlinear preservers on matrix domains\nby
Ilja Gogić (University of Zagreb\, Croatia) as part of European Non-Asso
ciative Algebra Seminar\n\n\nAbstract\nThe celebrated Kaplansky–Aupetit
conjecture asks whether\nevery surjective linear map between unital semisi
mple Banach algebras\nthat shrinks the spectrum must be a Jordan homomorph
ism. While the\nconjecture has been resolved in specific settings (most no
tably for\nvon Neumann algebras by Aupetit and for algebras of bounded lin
ear\noperators on Banach spaces by Sourour)\, it remains widely open\, eve
n\nfor C*-algebras. In contrast\, spectrum-preserving maps are often more\
naccessible\, and a natural question is whether results in that setting\nc
an be extended to the spectrum-shrinking case. However\, existing\nresults
indicate that such generalizations are typically far more\ndelicate. Moti
vated by this\, the talk investigates continuous\nspectrum-shrinking maps
from various subsets Xₙ of the complex matrix\nalgebra Mₙ with values
in another matrix algebra Mₘ. The classes of\ndomains Xₙ under conside
ration include structural matrix algebras\n(i.e. subalgebras of Mₙ conta
ining all diagonal matrices)\, the sets of\nnormal and singular matrices\,
and matrix Lie groups such as GL(n)\,\nSL(n)\, and U(n). Our first object
ive is to determine when such\nspectrum-shrinking maps automatically prese
rve the spectrum. Building\non this\, and Šemrl’s influential nonlinear
characterization of Jordan\nautomorphisms of Mₙ (when n ≥ 3) as conti
nuous maps preserving both\nspectrum and commutativity\, our second object
ive is to establish an\nanalogous nonlinear preserver theorem for maps X
ₙ → Mₙ. This is based\non joint work with Alexandru Chirvasitu (Univ
ersity at Buffalo) and\nMateo Tomašević (University of Zagreb).\n
LOCATION:https://researchseminars.org/talk/ENAAS/144/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Victor Roca i Lucio (Paris Cité University\, France)
DTSTART:20251020T150000Z
DTEND:20251020T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/145
DESCRIPTION:Title:
Higher Lie theory in positive characteristic\nby Victor Roca i Lucio (
Paris Cité University\, France) as part of European Non-Associative Algeb
ra Seminar\n\n\nAbstract\nGiven a nilpotent Lie algebra over a characteris
tic zero field\, one can construct a group in a universal way via the Bake
r-Campbell-Hausdorff formula. This integration procedure admits generaliza
tions to dg Lie or L-infinity-algebras\, giving in general infinity-groupo
id of deformations that it encodes\, as by the Lurie-Pridham correspondenc
e\, infinitesimal deformation problems are equivalent to dg Lie algebras.
The recent work of Brantner-Mathew establishes a correspondence between in
finitesimal deformation problems and partition Lie algebras over a positiv
e characteristic field. In this talk\, I will explain how to construct an
analogue of the integration functor for certain point-set models of (spect
ral) partition Lie algebras\, and how this integration functor can recover
the associated deformation problem under some assumptions. Furthermore\,
I will discuss some applications of these constructions to unstable p-adic
homotopy theory.\n
LOCATION:https://researchseminars.org/talk/ENAAS/145/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michiel Smet (Ghent University\, Belgium)
DTSTART:20251027T150000Z
DTEND:20251027T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/146
DESCRIPTION:Title:
Cubic norm pairs and hermitian cubic norm structures\nby Michiel Smet
(Ghent University\, Belgium) as part of European Non-Associative Algebra S
eminar\n\n\nAbstract\nCubic norm structures were originally introduced by
McCrimmon to generalize Springer's construction of Jordan algebras from a
pairing of cubic forms. These cubic norm structures appear naturally in th
e study of (exceptional) Lie algebras and (exceptional) linear algebraic g
roups. Later\, Allison introduced structurable algebras. One of the main c
lasses of structurable algebras is closely related to cubic norm structure
s. Moreover\, the natural appearances of cubic norm structures can often b
e understood in terms of this class of structurable algebras. To better un
derstand this class of structurable algebras\, De Medts introduced hermiti
an cubic norm structures.\nIn this talk\, we introduce cubic norm pairs an
d hermitian cubic norm structures over arbitrary commutative rings and con
struct an associated structurable algebra\, Lie algebra\, and automorphism
group. We also study the behaviour of certain automorphism groups.\n
LOCATION:https://researchseminars.org/talk/ENAAS/146/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiaomin Tang (Heilongjiang University\, China)
DTSTART:20251103T150000Z
DTEND:20251103T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/147
DESCRIPTION:Title:
Toroidal Cluster Algebra and the Toroidal Grothendieck ring of a tensor ca
tegory\nby Xiaomin Tang (Heilongjiang University\, China) as part of E
uropean Non-Associative Algebra Seminar\n\n\nAbstract\nLet U be the quantu
m loop algebra corresponding to a simple Lie algebra and K be the Grothen
dieck ring of a specific tensor category consisting of finite-dimensional
U-modules\, which possesses a natural cluster algebra structure. In this
talk\, we delineate a toroidal cluster structure endowed with two paramet
ers on the toroidal Grothendieck ring K of the monomial category C\, whic
h is intimately tied to the quantum loop algebra of type A3.\n
LOCATION:https://researchseminars.org/talk/ENAAS/147/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ginevra Giordani (University of L'Aquila\, Italy)
DTSTART:20251110T150000Z
DTEND:20251110T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/148
DESCRIPTION:Title:
Central exponent in PI-theory\nby Ginevra Giordani (University of L'Aq
uila\, Italy) as part of European Non-Associative Algebra Seminar\n\n\nAbs
tract\nThe algebras that satisfy at least a non-trivial polynomial identit
y are called PI-algebras. They can be seen as a generalization of the com
mutative world and PI-theory is the research field in modern algebra study
ing the identities satisfied by these algebras. In its general case this i
s a very difficult problem\, so that a combinatoric approach is generally
used. \n\nWe will briefly introduce polynomial identities and PI-algebras\
, giving also some motivations\, and we will present the main results in P
I-theory.\n\nThen\, we will introduce central polynomials\, explaining why
they are important for the research on polynomial indentities.\nTheir beh
avior can be also studied by analyzing the behavior of the dimension $c_n^
z(A)$ of the space of multilinear polynomials of degree $n$ modulo the cen
tral polynomials of an associative PI-algebra $A$. In 2018\, Giambruno and
Zaicev established\, for associative algebras\, the existence of the limi
t\n$$\n\\lim_{n \\to \\infty} \\sqrt[n]{c_n^z(A)}.\n$$\nIn this talk we pr
esent research advances on this problem\, with special focus on associativ
e superalgebras with superinvolution.\n\nThis talk is based on a joint wor
k with Antonio Ioppolo\, Antônio Augusto dos\nSantos and Ana Cristina Vie
ira.\n
LOCATION:https://researchseminars.org/talk/ENAAS/148/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iván Ruiz Campos (University of Málaga\, Spain)
DTSTART:20250908T150000Z
DTEND:20250908T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/149
DESCRIPTION:Title:
The affine group scheme of the automorphisms of evolution algebras of dime
nsion 2.\nby Iván Ruiz Campos (University of Málaga\, Spain) as part
of European Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk w
e establish a connection between evolution algebras of dimension two and H
opf algebras\, via the algebraic group of automorphisms of an evolution al
gebra. This analysis involves the computation of the (tight) p−algebra a
ssociated with any 2-dimensional evolution algebra\, whenever it exists. F
urthermore\, if A is perfect and has a faithful tight p-algebra\, then thi
s p-algebra is isomorphic to H (the Hopf algebra associated to the evoluti
on algebra).\n
LOCATION:https://researchseminars.org/talk/ENAAS/149/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yulia Zaitseva (HSE University\, Russia)
DTSTART:20251117T150000Z
DTEND:20251117T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/150
DESCRIPTION:Title:
Derivations on toric and trinomial algebras\nby Yulia Zaitseva (HSE Un
iversity\, Russia) as part of European Non-Associative Algebra Seminar\n\n
\nAbstract\nA derivation D on an algebra A is said to be locally nilpotent
if any element of A is annihilated by some power of D. If A is an algebra
of regular functions on an affine algebraic variety X\, then locally nilp
otent derivations on A correspond to actions of one-parameter unipotent su
bgroups on X. In turn\, actions of tori on X correspond to gradings on A.
I will survey some classification results about homogeneous locally nilpot
ent derivations on toric varieties and their generalizations.\n
LOCATION:https://researchseminars.org/talk/ENAAS/150/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerardo Martín Escolano (University of Granada\, Spain)
DTSTART:20251124T150000Z
DTEND:20251124T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/151
DESCRIPTION:Title:
Preserver Problems on Jordan Banach algebras and applications\nby Gera
rdo Martín Escolano (University of Granada\, Spain) as part of European N
on-Associative Algebra Seminar\n\n\nAbstract\nIn this talk we will discuss
about many topics related with preserver problems in Jordan Banach algebr
as\, in particular\, we will talk about the Lie-Trotter formula for Jordan
Banach algebras and its application in the study of spectral-valued multi
plicative functionals. Moreover we will present some results related with
maps preserving what is called strong commutativity or operator commutativ
ity. Finally\, we will discuss about the Mackey-Gleason problem for Jordan
Banach algebras and if time permits\, we will show how this result can be
applied in the study of piecewise Jordan homomorphism.\n
LOCATION:https://researchseminars.org/talk/ENAAS/151/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vicent Pérez Calabuig (University of Valencia\, Spain)
DTSTART:20251201T150000Z
DTEND:20251201T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/152
DESCRIPTION:Title:
On left nilpotent skew braces of class 2\nby Vicent Pérez Calabuig (U
niversity of Valencia\, Spain) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nIn this seminar\, a detailed study of left nilpote
nt skew braces B of class 2 will be carried out. We shall see that in the
case that B is of nilpotent type\, then it is centrally nilpotent\; in par
ticular\, if B is of abelian type then it is right nilpotent of class 3. T
his opens the door to know much more about the inner structure of left nil
potent skew braces of class 2 and its associated solution of the Yang-Baxt
er equation. In the abelian type case\, we shall delve into the descriptio
n of these finitely generated braces.\n
LOCATION:https://researchseminars.org/talk/ENAAS/152/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Azamat Saydaliyev (Institute of Mathematics\, Uzbekistan)
DTSTART:20251208T150000Z
DTEND:20251208T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/153
DESCRIPTION:Title:
Algebraic and geometric classification of non-associative algebras\nby
Azamat Saydaliyev (Institute of Mathematics\, Uzbekistan) as part of Euro
pean Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk\, we stud
y the algebraic and geometric classification of several families of non-as
sociative algebras\, including Jordan superalgebras\, F-manifold algebras\
, $\\delta$-Poisson algebras\, and transposed $\\delta$-Poisson algebras.
After briefly recalling the definitions and known results\, we compare the
ir algebraic and geometric classification. We conclude by presenting new c
lassification results obtained in our work.\n
LOCATION:https://researchseminars.org/talk/ENAAS/153/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristina Draper Fontanals (University of Málaga\, Spain)
DTSTART:20251215T150000Z
DTEND:20251215T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/154
DESCRIPTION:Title:
Revisiting simple Lie algebras from the view of the grading group\nby
Cristina Draper Fontanals (University of Málaga\, Spain) as part of Europ
ean Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk we discuss
the role of gradings on Lie algebras and how they can be used to obtain s
uitable models for a wide range of structures\, including simple\, solvabl
e\, and nilpotent Lie algebras. We introduce the notion of a \\emph{genera
lized group algebra}\, which provides a flexible framework for describing
graded algebras in full generality. Although this concept may at first app
ear too broad to be useful in the specific context of Lie algebras\, we sh
all show how naturally it applies by examining several illustrative exampl
es.\n\nA central theme will be the use of the \\emph{grading group} to gai
n insight into structural properties of the underlying Lie algebra. For in
stance\, viewing $\\mathfrak{so}(8)$ as a generalized group algebra sheds
light on its spin representations and on the phenomenon of triality. More
broadly\, this perspective greatly simplifies the construction of orthonor
mal bases\, as in the case of $\\mathfrak{g}_2$.\n\nFinally\, we show that
this approach renders the computation of brackets in Lie algebras obtaine
d via \\emph{graded contractions} essentially immediate. This leads to vas
t families of high-dimensional nonsimple Lie algebras with distinctive str
uctural features\, obtained from the exceptional simple Lie algebras throu
gh the Tits construction.\n
LOCATION:https://researchseminars.org/talk/ENAAS/154/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mateo Tomašević (University of Zagreb\, Croatia)
DTSTART:20260105T150000Z
DTEND:20260105T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/155
DESCRIPTION:Title:
Automatic additivity of multiplicative and Jordan multiplicative maps\
nby Mateo Tomašević (University of Zagreb\, Croatia) as part of European
Non-Associative Algebra Seminar\n\n\nAbstract\nIn this talk\, we discuss
the problem of automatic additivity for multiplicative maps between rings\
, following the classical results of Martindale and Jodeit-Lam. We present
a complete description of Jordan multiplicative self-maps on full matrix
algebras M_n(F)\, where F is a field of characteristic not equal to 2. Wit
hout imposing additional assumptions\, we show that such maps are either c
onstant (and equal to a fixed idempotent)\, or additive (and hence Jordan
monomorphisms). This result is joint work with Ilja Gogić.\n
LOCATION:https://researchseminars.org/talk/ENAAS/155/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramón González Rodríguez (University of Vigo\, Spain)
DTSTART:20260112T150000Z
DTEND:20260112T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/156
DESCRIPTION:Title:
Quasigroupoids and weak Hopf quasigroups\nby Ramón González Rodrígu
ez (University of Vigo\, Spain) as part of European Non-Associative Algebr
a Seminar\n\n\nAbstract\nQuasigroupoids and weak Hopf quasigroups are non
associative generalizations of groupoids and weak Hopf algebras. In this t
alk we will show that the category of finite quasigroupoids is equivalent
to the one of pointed cosemisimple weak Hopf quasigroups over a given fie
ld K. As a consequence\, we obtain a categorical equivalence between the
categories of quasigroups\, in the sense of Klim and Majid (i.e.\, loops w
ith the inverse property)\, and the category of pointed cosemisimple Hopf
quasigroups over K. On the other hand\, in this talk we introduce the not
ion of exact factorization of a quasigroupoid and the notion of matched p
air of quasigroupoids with common base. We prove that if (A\,H) is a match
ed pair of quasigroupoids it is posible to construct a new quasigroupoid
called the double cross product of A and H. Moreover\, we show that\, if
a quasigroupoid B admits an exact factorization\, there exists a matched
pair of quasigroupoids (A\,H) and an isomorphism of quasigroupoids betw
een the double cross product of A and H and B. Finally\, we show that eve
ry matched pair of quasigroupoids (A\,H) induces\, thanks to the quasigrou
poid magma construction\, a pair (K[A]\, K[H]) of weak Hopf quasigroups an
d a double crossed product of weak Hopf quasigroups isomorphic as weak Hop
f quasigroups to the quasigroupoid magma of the double cross product gor
upoid of A and H .\n
LOCATION:https://researchseminars.org/talk/ENAAS/156/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimitar Grantcharov (University of Texas at Arlington\, USA)
DTSTART:20260119T150000Z
DTEND:20260119T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/157
DESCRIPTION:Title:
U(h)-Free sl(2)-Modules of rank 2\nby Dimitar Grantcharov (University
of Texas at Arlington\, USA) as part of European Non-Associative Algebra S
eminar\n\n\nAbstract\nIn this talk\, we will discuss non-weight modules ov
er the Lie algebra sl(2). More precisely\, we focus on modules that are fr
ee of finite rank over the universal enveloping algebra U(h) of a Cartan s
ubalgebra h of sl(2). In particular\, we will present a new family of simp
le U(h)-free modules of rank 2. The talk is based on joint work with K. Ng
uyen and K. Zhao.\n
LOCATION:https://researchseminars.org/talk/ENAAS/157/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernardo Leite da Cunha (University of Santiago de Compostela\, Sp
ain)
DTSTART:20260126T150000Z
DTEND:20260126T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/158
DESCRIPTION:Title:
Representations of two-dimensional compatible Lie algebras\nby Bernard
o Leite da Cunha (University of Santiago de Compostela\, Spain) as part of
European Non-Associative Algebra Seminar\n\n\nAbstract\nA compatible Lie
algebra is a vector space equipped with two Lie products such that any lin
ear combination of them is also a Lie product. These algebras arose from t
he related class of compatible Poisson algebras in the context of mathemat
ical physics and Hamiltonian mechanics.\nIn this talk\, we start by statin
g some basic definitions and results about compatible Lie algebras. We the
n present counterexamples to analogues of some of the most important theor
ems in Lie algebra theory\, namely the theorems of Weyl and Levi\, highlig
hting how compatible Lie algebras can behave very differently from Lie alg
ebras.\nWe then move on to studying the representation theory of a family
of simple two-dimensional compatible Lie algebras. We construct a family o
f irreducible representations for each algebra of this family\, and therea
fter\, we focus on one specific simple two-dimensional compatible Lie alge
bra in order to make the computations simpler and results easier to state
and prove. In this setting\, we prove a Clebsch-Gordan formula for the irr
educible representations previously described\, and we also exhibit a seco
nd family of representations\, this time "breaking" Weyl's theorem (i.e.\,
reducible and indecomposable representations over the field of complex nu
mbers).\nTime permitting\, we finish by discussing the failure of further
central results from Lie algebra theory in this broader context\, includin
g the characterization of semisimple algebras and the Whitehead Lemmas.\n
LOCATION:https://researchseminars.org/talk/ENAAS/158/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zahra Nazemian (University of Graz\, Austria)
DTSTART:20260202T150000Z
DTEND:20260202T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/159
DESCRIPTION:Title:
Aut-stable subspaces of algebras and beyond\nby Zahra Nazemian (Univer
sity of Graz\, Austria) as part of European Non-Associative Algebra Semina
r\n\n\nAbstract\nIn this talk\, we recall some challenging problems in alg
ebra\, such as the characterization problem of polynomial rings\, the auto
morphism groups of certain algebras\, and the Dixmier property of algebras
. We then explain how the concept of Aut-stable subspaces can be used as a
tool to approach these problems.\n
LOCATION:https://researchseminars.org/talk/ENAAS/159/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hans Cuypers (Eindhoven University of Technology\, Netherlands)
DTSTART:20260209T150000Z
DTEND:20260209T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/160
DESCRIPTION:Title:
Every group is automorphism group of a simple algebra\nby Hans Cuypers
(Eindhoven University of Technology\, Netherlands) as part of European No
n-Associative Algebra Seminar\n\n\nAbstract\nPopov raised the question wh
ether each finite group is the automorphism group of a finite dimensional
simple algebra. He and Gordeev provided an affirmative answer for suffici
ently large enough fields\, not only for finite groups\, but also for alge
braic groups. We will show that for each field F and each (finite) group
G there are infinitely many (finite) dimensional simple algebras with G
as automorphism group. If F has at least 4 elements the algebras can be
commutative as well as non-commutative.\n
LOCATION:https://researchseminars.org/talk/ENAAS/160/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Davide Ferri (University of Torino\, Italy)
DTSTART:20260216T150000Z
DTEND:20260216T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/161
DESCRIPTION:Title:
From sets to quivers: oidification and the Yang-Baxter equation\nby Da
vide Ferri (University of Torino\, Italy) as part of European Non-Associat
ive Algebra Seminar\n\n\nAbstract\nThe Yang-Baxter equation\, or braid rel
ation\, can be defined in any monoidal category. In the category Set\, muc
h is known about its solutions. In this seminar I describe the monoidal ca
tegory Quiv_\\Lambda of quivers over a fixed set of vertices \\Lambda. I i
ntroduce the philosophy called "oidification"\, which turns sets into quiv
ers\, groups into groupoids\, algebras into algebroids\, etc. Finally\, I
give an overview of the theory of the Yang-Baxter equation in Quiv_\\Lambd
a\, why it is relevant\, what still works as in Set (and what works better
than in Set!)\, and how it relates to the theory of partial solutions and
partial algebraic structures.\n
LOCATION:https://researchseminars.org/talk/ENAAS/161/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Saikat Goswami (Institute for Advancing Intelligence\, India)
DTSTART:20260223T150000Z
DTEND:20260223T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/162
DESCRIPTION:Title:
Universal Constructions on Algebras over Operads\nby Saikat Goswami (I
nstitute for Advancing Intelligence\, India) as part of European Non-Assoc
iative Algebra Seminar\n\n\nAbstract\nWe construct a universal coacting bi
algebra and Hopf algebra for any finite-dimensional algebra over a symmetr
ic operad. This work extends previous constructions of Agore and Militaru
to the operadic setting. We show that the category of finite-dimensional a
lgebras over operads is enriched over the dual of commutative algebras\, w
hich induces a canonical bialgebra structure on the associated universal c
oacting algebra. Our framework recovers known constructions for Lie\, Leib
niz\, and Poisson algebras\, offering a unified operadic perspective on co
acting objects across a broad class of algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/162/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Adam Chapman (Academic College of Tel-Aviv-Yaffo\, Israel)
DTSTART:20260302T150000Z
DTEND:20260302T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/163
DESCRIPTION:Title:
Measuring the associativity of loops\nby Adam Chapman (Academic Colleg
e of Tel-Aviv-Yaffo\, Israel) as part of European Non-Associative Algebra
Seminar\n\n\nAbstract\nIn group theory folklore\, there is a well-known th
eorem\; The probability that two randomly uniformly chosen elements commut
e in a non-abelian group $G$ cannot exceed 5/8. The bound is attained by t
he Quaternion group $Q_8$. In this talk\, we shall discuss a non-associati
ve analog of the theorem. Namely\, the probability of three randomly chose
n elements associating is bounded by 43/64 in Moufang loops with nuclear c
ommutators\, with the bound attained by the Octonion loop $O_{16}$.\n
LOCATION:https://researchseminars.org/talk/ENAAS/163/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucia Bagnoli (Sapienza University of Rome\, Italy)
DTSTART:20260309T150000Z
DTEND:20260309T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/164
DESCRIPTION:Title:
On new classes of quantum vertex algebras\nby Lucia Bagnoli (Sapienza
University of Rome\, Italy) as part of European Non-Associative Algebra Se
minar\n\n\nAbstract\nWe present the construction of a new class of quantum
vertex algebras associated with a normalized Yang R-matrix. They are obta
ined as Yangian deformations of certain S-commutative quantum vertex algeb
ras and their S-locality takes the form of a single RTT relation. We estab
lish some preliminary results on their representation theory and then furt
her investigate their braiding map. These results were obtained jointly wi
th Slaven Kožić. Then we will discuss a recent generalization of these r
esults to the case of the type A trigonometric R-matrix. These results wer
e obtained jointly with Marijana Butorac and Slaven Kožić.\n
LOCATION:https://researchseminars.org/talk/ENAAS/164/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carsten Dietzel (University of Caen Normandy\, France)
DTSTART:20260316T150000Z
DTEND:20260316T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/165
DESCRIPTION:Title:
A Brief Guide to Cabling and Endocabling.\nby Carsten Dietzel (Univers
ity of Caen Normandy\, France) as part of European Non-Associative Algebra
Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n
\nAbstract\nCabling is a method developed by Lebed\, Ramìrez and Vendrami
n to deform involutive\, non-degenerate solutions to the Yang-Baxter equat
ions while keeping control over the diagonal maps of the resulting solutio
ns. This powerful tool allows one to prove a plethora of decomposability r
esults for involutive solutions and has recently been generalized by Colaz
zo and Van Antwerpen to obtain similar results for non-involutive solution
s. In this talk\, I will give an outline of classical cabling in the style
of Lebed\, Ramìrez and Vendramin\, and explain some standard application
s of the method. Afterwards\, I will demonstrate how classical cabling can
be generalized to endocabling\, where involutive solutions are deformed b
y means of endomorphisms of the module structure of permutation braces whi
ch is given by the λ-action. Finally\, I will give a rough sketch how end
ocabling can be applied to provide insights into the structure of solution
s whose diagonal map is a cyclic permutation.\n
LOCATION:https://researchseminars.org/talk/ENAAS/165/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:István Heckenberger (Philipps University Marburg\, Germany)
DTSTART:20261012T150000Z
DTEND:20261012T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/166
DESCRIPTION:Title:
Pointed Hopf algebras of odd dimension\nby István Heckenberger (Phili
pps University Marburg\, Germany) as part of European Non-Associative Alge
bra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/780318106
4\n\nAbstract\nIn joint work with Andruskiewitsch and Vendramin we proved
that over algebraically closed fields of characteristic zero\, pointed Hop
f algebras of odd dimension are cocycle deformations of bosonizations of N
ichols algebras of diagonal type. The proof is based on deep results of se
veral people about pointed Hopf algebras with abelian coradical\, and on a
new deformation argument for solvable groups. I will explain the notions
in the theorem and give some details about the proof.\n
LOCATION:https://researchseminars.org/talk/ENAAS/166/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Willian Franca (Federal University of Juiz de Fora\, Brazil)
DTSTART:20260330T150000Z
DTEND:20260330T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/167
DESCRIPTION:Title:
Applications of compact multipliers to algebrability of $(\\ell_{\\infty}\
\setminus c_0)\\cup\\{0\\}$ and $(B(\\ell_2(\\mathbb{N}))\\setminus K(\\el
l_2(\\mathbb{N}))\\cup \\{ 0\\}.$\nby Willian Franca (Federal Universi
ty of Juiz de Fora\, Brazil) as part of European Non-Associative Algebra S
eminar\n\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n\n
Abstract\nIn present talk we deal with the class $\\mathcal{C}=\\mathcal{C
}_1\\cup \\mathcal{C}_2$ where $\\mathcal{C}_1$ (respectively\, $\\mat
hcal{C}_2$) is formed by all separable Uniform algebras (respectively\, s
eparable commutative C$^*$-algebras) with no compact elements. For a giv
en algebra $A$ in $\\mathcal{C}_1$ (respectively\, $A$ in $\\mathcal{C}_2
$) we will show that $A$ is isometrically isomorphic as algebra (respecti
vely\, as C$^*$-algebra) to a subalgebra $M$ of $\\ell_{\\infty}$ with $M\
\subset (\\ell_{\\infty}\\setminus c_0)\\cup\\{0\\}.$ Under the additional
assumption that $A$ is non-unital we verify that there exists a copy of
$M(A)$ (the multipliers algebra of $A$ which is non-separable) inside $(\\
ell_{\\infty}\\setminus c_0)\\cup\\{0\\}$.\n\nFor an infinitely generated
abelian C$^*$-algebra $B\,$ we will study the least cardinality possible o
f a system of generators ($\\gn_{C^*}(B)$). In fact we will deduce that $\
\gn_{C^*}(B)$ coincides with the smallest cardinal number $n$ such that a
n embedding of $\\Delta(B)$ (= the spectrum of $B$) in $\\mathbb{R}^n$ e
xists - The finitely generated version of this result was proved by Nagis
a.\nIn addition\, we will introduce new concepts of algebrability in term
s of $\\gn_{C^*}(B)$ ($(C^*)$-genalgebrability) and its natural variations
.\n\nFrom our methods we will infer that there is $^*$-isomorphic copy of
$\\ell_{\\infty}$ in $(\\ell_{\\infty}\\setminus c_0)\\cup\\{0\\}$. In par
ticular\, $(\\ell_{\\infty}\\setminus c_0)\\cup\\{0\\}$ contains a copy of
every separable Banach space.\nMoreover\, all the positive answers of th
is work holds if we replace the set $(\\ell_{\\infty}\\setminus c_0)\\cup\
\{0\\}$ with $(B(\\ell_2(\\mathbb{N}))\\setminus K(\\ell_2(\\mathbb{N}))\\
cup \\{ 0\\}.$\n\nThis is a joint work with Jorge J. Garcés (Universidad
Politécnica de Madrid)\n
LOCATION:https://researchseminars.org/talk/ENAAS/167/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rong Tang (Jilin University\, China)
DTSTART:20260406T150000Z
DTEND:20260406T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/168
DESCRIPTION:Title:
Homotopy theory of post-Lie algebras\nby Rong Tang (Jilin University\,
China) as part of European Non-Associative Algebra Seminar\n\nInteractive
livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract\nGuided by K
oszul duality theory\, we consider the graded Lie algebra of coderivations
of the cofree conilpotent graded cocommutative cotrialgebra generated by
$V$. We show that in the case of $V$ being a shift of an ungraded vector s
pace $W$\, Maurer-Cartan elements of this graded Lie algebra are exactly
post-Lie algebra structures on $W$. The cohomology of a post-Lie algebra
is then defined using Maurer-Cartan twisting. The second cohomology group
of a post-Lie algebra has a familiar interpretation as equivalence classes
of infinitesimal deformations. Next we define a post-Lie$_\\infty$ algebr
a structure on a graded vector space to be a Maurer-Cartan element of the
aforementioned graded Lie algebra. Post-Lie$_\\infty$ algebras admit a us
eful characterization in terms of $L_\\infty$-actions (or open-closed homo
topy Lie algebras). Finally\, we introduce the notion of homotopy Rota-Bax
ter operators on open-closed homotopy Lie algebras and show that certain h
omotopy Rota-Baxter operators induce post-Lie$_\\infty$ algebras. This is
a joint work with Andrey Lazarev and Yunhe Sheng.\n
LOCATION:https://researchseminars.org/talk/ENAAS/168/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maria Ferrara (Pegaso University\, Italy)
DTSTART:20260413T150000Z
DTEND:20260413T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/169
DESCRIPTION:Title:
A Sylow Theorem for Some Classes of Finite Skew Braces\nby Maria Ferra
ra (Pegaso University\, Italy) as part of European Non-Associative Algebra
Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n
\nAbstract\nWe study a skew brace analogue of the First Sylow Theorem for
finite groups. Although a general version of this result is not yet availa
ble in the context of skew braces\, we show that it holds for several nota
ble classes of finite skew braces\, including the supersolvable ones. This
work is carried out in collabora- tion with Andrea Caranti\, Ilaria Del C
orso\, Massimiliano Di Matteo\, and Marco Trombetti.\n
LOCATION:https://researchseminars.org/talk/ENAAS/169/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Lau (Laval University\, Canada)
DTSTART:20260420T150000Z
DTEND:20260420T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/170
DESCRIPTION:Title:
Lie algebra representations and free Jordan algebras\nby Michael Lau (
Laval University\, Canada) as part of European Non-Associative Algebra Sem
inar\n\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n\nAb
stract\nFor any unital Jordan algebra\, the famous Tits-Kantor-Koecher con
struction produces an sl(2)-graded Lie algebra. We will look at weight mo
dules for universal central extensions of these algebras\, concentrating o
n categories of modules satisfying combinatorial dominance or smoothness c
onditions. We describe some finiteness results for algebras and Weyl modu
les in these contexts. Surprisingly\, the proofs of several of our result
s use Zelmanov's theorem on nil Jordan algebras of bounded index. This ta
lk is based on joint work with Olivier Mathieu.\n
LOCATION:https://researchseminars.org/talk/ENAAS/170/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abdenacer Makhlouf (University of Haute Alsace\, France)
DTSTART:20260427T150000Z
DTEND:20260427T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/171
DESCRIPTION:by Abdenacer Makhlouf (University of Haute Alsace\, France) as
part of European Non-Associative Algebra Seminar\n\nInteractive livestrea
m: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/171/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Per Bäck (Mälardalen University\, Sweden)
DTSTART:20260504T150000Z
DTEND:20260504T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/172
DESCRIPTION:Title:
Hilbert’s Basis Theorem for Noncommutative\, Nonassociative Polynomial R
ings\nby Per Bäck (Mälardalen University\, Sweden) as part of Europe
an Non-Associative Algebra Seminar\n\nInteractive livestream: https://us02
web.zoom.us/j/7803181064\n\nAbstract\nIn this talk\, I will introduce Ore
extensions\, the principal noncommutative generalization of polynomial rin
gs\, and recall how Hilbert’s Basis Theorem extends to them. I will then
present generalized nonassociative Ore extensions (GNOEs)\, a natural ext
ension of Ore extensions to the nonassociative setting that provides a uni
fying framework for nonassociative\, noncommutative polynomial rings\, inc
luding examples such as the Cayley–Dickson algebras. Finally\, I will sh
ow that Hilbert’s Basis Theorem generalizes to GNOEs via the existence o
f Euclidean division algorithms\, revealing a new and direct connection be
tween such algorithms and the left and right Noetherianity of these rings.
This talk is based on joint work with Masood Aryapoor.\n
LOCATION:https://researchseminars.org/talk/ENAAS/172/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Krzysztof Radziszewski (University of Białystok\, Poland)
DTSTART:20260511T150000Z
DTEND:20260511T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/173
DESCRIPTION:Title:
Affinization of algebraic structures\nby Krzysztof Radziszewski (Unive
rsity of Białystok\, Poland) as part of European Non-Associative Algebra
Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n\
nAbstract\nInformally and in broad terms\, by affinization we mean a proce
ss which converts an algebraic structure with a nullary operation (i.e. in
which a chosen element plays special role) into one which has no nullary
operations\, but is such that by a free choice of any element it is retrac
ted to the original structure. The prime example of this procedure is the
conversion of groups into heaps. In this talk we will focus mainly on affi
nization of Lie algebras and Leibniz algebras. The talk is based on joint
works with Tomasz Brzeziński\, Ryszard Andruszkiewicz and Brais Ramos Per
ez.\n
LOCATION:https://researchseminars.org/talk/ENAAS/173/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ágota Figula (University of Debrecen\, Hungary)
DTSTART:20260518T150000Z
DTEND:20260518T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/174
DESCRIPTION:Title:
Malcev-like anti-commutative algebras\nby Ágota Figula (University of
Debrecen\, Hungary) as part of European Non-Associative Algebra Seminar\n
\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract
\nThe tangent algebras of local analytic Moufang and diassociative loops a
re Malcev algebras and binary Lie algebras introduced by A. I. Malcev. The
ir classifications in low dimension are given by the works on E. N. Kuzmin
and A. T. Gainov. In the talk we discuss the classification of solvable a
nti-commutative algebras that have the same decomposition properties as so
lvable Malcev or binary Lie algebras. The classification result enables us
to find and study a family of binary Lie algebras for which the closed fo
rm of the Baker-Campbell- Hausdorff series defines the multiplication func
tion of an analytic diassociative loop on the entire binary Lie algebra.\n
LOCATION:https://researchseminars.org/talk/ENAAS/174/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrés Pérez-Rodríguez (University of Santiago de Compostela\,
Spain)
DTSTART:20260525T150000Z
DTEND:20260525T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/175
DESCRIPTION:Title:
Lattice-theoretical aspects of evolution algebras\nby Andrés Pérez-R
odríguez (University of Santiago de Compostela\, Spain) as part of Europe
an Non-Associative Algebra Seminar\n\nInteractive livestream: https://us02
web.zoom.us/j/7803181064\n\nAbstract\nLattice theories have been developed
in several algebraic structures\, such as groups and Lie algebras\; howev
er\, this is not the case for evolution algebras\, which are commutative b
ut nonassociative structures introduced by Tian and Vojtěchovský in 2006
to model non-Mendelian inheritance. Motivated by this\, in this talk we s
tudy the subalgebra lattices of solvable evolution algebras\, focusing on
two classical lattice-theoretical properties: distributivity and modularit
y. Subsequently\, we turn to maximal subalgebras\, whose intersection is t
raditionally known as the Frattini subalgebra. This resulting Frattini the
ory allows us to investigate intrinsic properties and to characterise dual
ly atomistic evolution algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/175/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Geoffrey Powell (University of Angers\, France)
DTSTART:20260601T150000Z
DTEND:20260601T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/176
DESCRIPTION:by Geoffrey Powell (University of Angers\, France) as part of
European Non-Associative Algebra Seminar\n\nInteractive livestream: https:
//us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/176/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Dimitrov (Queen’s University\, Canada)
DTSTART:20260608T150000Z
DTEND:20260608T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/177
DESCRIPTION:Title:
U(h)-free modules over the Lie superalgebras sl(m|n)\nby Ivan Dimitrov
(Queen’s University\, Canada) as part of European Non-Associative Algeb
ra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/7803181064
\n\nAbstract\nIn this talk I will discuss the existence and classification
of certain classes of sl(m|n)-modules which when restricted to the univer
sal enveloping algebra U(h) of a Cartan subalgebra h are free of finite ra
nk. Particular results include: Classification of modules of rank 2\; exis
tence and structure of modules of higher rank\; weight modules obtained fr
om U(h)-free modules via the weighting functor.\n
LOCATION:https://researchseminars.org/talk/ENAAS/177/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rinat Kashaev (University of Geneva\, Switzerland)
DTSTART:20260615T150000Z
DTEND:20260615T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/178
DESCRIPTION:Title:
Braided Hopf algebra structures on exterior algebras\nby Rinat Kashaev
(University of Geneva\, Switzerland) as part of European Non-Associative
Algebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/78031
81064\n\nAbstract\nThe exterior algebra of any vector space of dimension g
reater than one admits a one-parameter family of braided Hopf algebra stru
ctures\, of which the standard super Hopf algebra structure is a particula
r example. By employing a one-parameter family of diagonal automorphisms o
f these braided Hopf algebras\, we construct solutions of the (constant) Y
ang-Baxter equation. These solutions conjecturally underlie the two-variab
le Links-Gould knot invariants associated with quantum supergroups. This i
s joint work with Vladimir Mangazeev.\n
LOCATION:https://researchseminars.org/talk/ENAAS/178/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:María Cueto-Avellaneda (University of Murcia\, Spain)
DTSTART:20260622T150000Z
DTEND:20260622T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/179
DESCRIPTION:by María Cueto-Avellaneda (University of Murcia\, Spain) as p
art of European Non-Associative Algebra Seminar\n\nInteractive livestream:
https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/179/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Atabey Kaygun (Istanbul Technical University\, Turkey)
DTSTART:20260706T150000Z
DTEND:20260706T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/180
DESCRIPTION:by Atabey Kaygun (Istanbul Technical University\, Turkey) as p
art of European Non-Associative Algebra Seminar\n\nInteractive livestream:
https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/180/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marco Castelli (University of Salento\, Italy)
DTSTART:20260713T150000Z
DTEND:20260713T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/181
DESCRIPTION:Title:
The impact of the diagonal permutation on involutive set-theoretic solutio
ns of the Yang–Baxter Equation\nby Marco Castelli (University of Sal
ento\, Italy) as part of European Non-Associative Algebra Seminar\n\nInter
active livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract\nSince
Drinfeld’s 1992 proposal to study the set-theoretic version of the Yang
–Baxter equation\, involutive solutions have attracted considerable atte
ntion. It is well known that to every non- degenerate involutive solution
one can associate a permutation\, referred to in the literature as the “
diagonal permutation”. The aim of this talk is to show how this single p
ermutation has a strong influence on the structure of (indecomposable) inv
olutive set-theoretic solutions. Some of the results presented are part of
a joint work with A. Kanrar.\n
LOCATION:https://researchseminars.org/talk/ENAAS/181/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marijana Butorac (University of Rijeka\, Croatia)
DTSTART:20260727T150000Z
DTEND:20260727T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/182
DESCRIPTION:Title:
Quasi-particle bases of standard modules for affine Lie algebras\nby M
arijana Butorac (University of Rijeka\, Croatia) as part of European Non-A
ssociative Algebra Seminar\n\nInteractive livestream: https://us02web.zoom
.us/j/7803181064\n\nAbstract\nCharacters of Feigin-Stoyanovsky's principal
subspaces of affine integrable highest weight modules are related with th
e sum sides of Rogers-Ramanujan-type identities. In this talk I will dis
cuss the construction of combinatorial bases of standard modules\, which r
elies on the the construction of quasi-particle bases of principal subspac
es. From quasi-particle bases we obtain characters of certain standard mod
ules of affine Lie algebra of type $B_l^{(1)}$. This talk is based on join
t works with Slaven Ko\\v zi\\' c and Mirko Primc.\n
LOCATION:https://researchseminars.org/talk/ENAAS/182/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Diogo Diniz (Federal University of Campina Grande\, Brazil)
DTSTART:20260810T150000Z
DTEND:20260810T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/183
DESCRIPTION:Title:
Graded Identities of Finite Matrices\nby Diogo Diniz (Federal Universi
ty of Campina Grande\, Brazil) as part of European Non-Associative Algebra
Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n
\nAbstract\nPolynomial identities of matrix algebras play a fundamental ro
le in the study of algebraic structures. In this talk\, we focus on the cl
assification of group gradings on $M_n(F)$\, when $F$ is a finite field\,
and on the description of the graded polynomial identities satisfied by $M
_n(F)$.\n
LOCATION:https://researchseminars.org/talk/ENAAS/183/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jethro van Ekeren (Institute of Pure and Applied Mathematics\, Bra
zil)
DTSTART:20260824T150000Z
DTEND:20260824T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/184
DESCRIPTION:Title:
Modular data of boundary W-algebras\nby Jethro van Ekeren (Institute o
f Pure and Applied Mathematics\, Brazil) as part of European Non-Associati
ve Algebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/78
03181064\n\nAbstract\nThe affine W-algebras form an important class of inf
inite dimensional algebras with applications in integrable systems and geo
metric representation theory. A special role is played in the theory by W-
algebras of "boundary level"\, in the sense that certain features of the r
epresentation theory of W-algebras in general can be determined once the b
oundary case is understood. I will discuss joint work with T. Arakawa\, I.
Blatt and W.-B. Yan in which we determine the tensor product structure of
boundary W-algebras in type A.\n
LOCATION:https://researchseminars.org/talk/ENAAS/184/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Kinyon (University of Denver\, USA)
DTSTART:20260629T150000Z
DTEND:20260629T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/185
DESCRIPTION:by Michael Kinyon (University of Denver\, USA) as part of Euro
pean Non-Associative Algebra Seminar\n\nInteractive livestream: https://us
02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/185/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yannic Vargas (CUNEF University\, Spain)
DTSTART:20260720T150000Z
DTEND:20260720T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/186
DESCRIPTION:by Yannic Vargas (CUNEF University\, Spain) as part of Europea
n Non-Associative Algebra Seminar\n\nInteractive livestream: https://us02w
eb.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/186/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Elad Paran (The Open University of Israel\, Israel)
DTSTART:20260803T150000Z
DTEND:20260803T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/187
DESCRIPTION:by Elad Paran (The Open University of Israel\, Israel) as part
of European Non-Associative Algebra Seminar\n\nInteractive livestream: ht
tps://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/187/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Silvia Properzi (Vrije Universiteit Brussel\, Belgium)
DTSTART:20261005T150000Z
DTEND:20261005T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/188
DESCRIPTION:by Silvia Properzi (Vrije Universiteit Brussel\, Belgium) as p
art of European Non-Associative Algebra Seminar\n\nInteractive livestream:
https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/188/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Quentin Ehret (New York University Abu Dhabi\, United Arab Emirat
es)
DTSTART:20260907T150000Z
DTEND:20260907T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/189
DESCRIPTION:by Quentin Ehret (New York University Abu Dhabi\, United Arab
Emirates) as part of European Non-Associative Algebra Seminar\n\nInteract
ive livestream: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/189/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lực Ta (University of Pittsburgh\, USA)
DTSTART:20260817T150000Z
DTEND:20260817T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/190
DESCRIPTION:Title:
From affine algebraic racks to Leibniz algebras and Yang–Baxter operator
s\nby Lực Ta (University of Pittsburgh\, USA) as part of European No
n-Associative Algebra Seminar\n\nInteractive livestream: https://us02web.z
oom.us/j/7803181064\n\nAbstract\nA version of Loday's "coquecigrue" proble
m over arbitrary ground fields seeks analogues of affine algebraic groups
whose tangent spaces are Leibniz algebras. To that end\, we construct func
tors assigning left and right Leibniz algebras to pointed rack objects in
the category of affine schemes. These functors have many desirable propert
ies\; in particular\, they recover the Lie algebras of linear algebraic gr
oups (via conjugation quandles) and the Leibniz algebras of algebraic Lie
racks. We also use rack schemes to functorially construct (co-)nondegenera
te solutions to the Yang–Baxter equation in the categories of schemes\,
sets\, and commutative k-algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/190/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Albano (University of Salento\, Italy)
DTSTART:20260323T150000Z
DTEND:20260323T160000Z
DTSTAMP:20260315T025928Z
UID:ENAAS/191
DESCRIPTION:Title:
Set-theoretic solutions of the Yang--Baxter equation and di-skew braces.\nby Andrea Albano (University of Salento\, Italy) as part of European N
on-Associative Algebra Seminar\n\nInteractive livestream: https://us02web.
zoom.us/j/7803181064\n\nAbstract\nThe aim of this talk is to provide a bri
ef overview of the role of generalised digroups in the study of the set-th
eoretic Yang-Baxter equation (YBE). Digroups are algebraic objects endowed
with two binary associative operations that arose in the investigations o
f R. Felipe\, K. Liu and M. Kinyon around the so-called coquecigrue proble
m\, as first stated by J. L. Loday. In detail\, we will introduce the stru
cture of di-skew braces as a split notion of usual skew braces and show ho
w they provide a class of non-degenerate solutions to the set-theoretic YB
E whose (left) derived rack is not necessarily idempotent. Moreover\, we w
ill describe basic properties of such solutions through the lens of self-d
istributivity and explore related ideas. Based on a joint work with Paola
Stefanelli.\n
LOCATION:https://researchseminars.org/talk/ENAAS/191/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
END:VCALENDAR