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BEGIN:VEVENT
SUMMARY:Alberto Elduque (University of Zaragoza\, Spain)
DTSTART;VALUE=DATE-TIME:20230109T150000Z
DTEND;VALUE=DATE-TIME:20230109T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230116T150000Z
DTEND;VALUE=DATE-TIME:20230116T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230123T150000Z
DTEND;VALUE=DATE-TIME:20230123T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230130T150000Z
DTEND;VALUE=DATE-TIME:20230130T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230206T150000Z
DTEND;VALUE=DATE-TIME:20230206T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230213T150000Z
DTEND;VALUE=DATE-TIME:20230213T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230220T150000Z
DTEND;VALUE=DATE-TIME:20230220T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230227T150000Z
DTEND;VALUE=DATE-TIME:20230227T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230306T150000Z
DTEND;VALUE=DATE-TIME:20230306T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230313T150000Z
DTEND;VALUE=DATE-TIME:20230313T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230320T150000Z
DTEND;VALUE=DATE-TIME:20230320T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230327T150000Z
DTEND;VALUE=DATE-TIME:20230327T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230410T150000Z
DTEND;VALUE=DATE-TIME:20230410T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230529T150000Z
DTEND;VALUE=DATE-TIME:20230529T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230417T150000Z
DTEND;VALUE=DATE-TIME:20230417T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230403T150000Z
DTEND;VALUE=DATE-TIME:20230403T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230522T150000Z
DTEND;VALUE=DATE-TIME:20230522T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230508T090000Z
DTEND;VALUE=DATE-TIME:20230508T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230508T150000Z
DTEND;VALUE=DATE-TIME:20230508T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230605T150000Z
DTEND;VALUE=DATE-TIME:20230605T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230515T090000Z
DTEND;VALUE=DATE-TIME:20230515T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230424T150000Z
DTEND;VALUE=DATE-TIME:20230424T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230612T150000Z
DTEND;VALUE=DATE-TIME:20230612T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230626T150000Z
DTEND;VALUE=DATE-TIME:20230626T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230703T150000Z
DTEND;VALUE=DATE-TIME:20230703T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230515T150000Z
DTEND;VALUE=DATE-TIME:20230515T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230424T090000Z
DTEND;VALUE=DATE-TIME:20230424T100000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230821T150000Z
DTEND;VALUE=DATE-TIME:20230821T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230814T150000Z
DTEND;VALUE=DATE-TIME:20230814T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230828T150000Z
DTEND;VALUE=DATE-TIME:20230828T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230710T150000Z
DTEND;VALUE=DATE-TIME:20230710T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230724T150000Z
DTEND;VALUE=DATE-TIME:20230724T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230717T150000Z
DTEND;VALUE=DATE-TIME:20230717T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230731T150000Z
DTEND;VALUE=DATE-TIME:20230731T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230807T150000Z
DTEND;VALUE=DATE-TIME:20230807T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230904T150000Z
DTEND;VALUE=DATE-TIME:20230904T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230911T150000Z
DTEND;VALUE=DATE-TIME:20230911T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230925T150000Z
DTEND;VALUE=DATE-TIME:20230925T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20231002T150000Z
DTEND;VALUE=DATE-TIME:20231002T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20230918T150000Z
DTEND;VALUE=DATE-TIME:20230918T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20231030T150000Z
DTEND;VALUE=DATE-TIME:20231030T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20231009T150000Z
DTEND;VALUE=DATE-TIME:20231009T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20231023T150000Z
DTEND;VALUE=DATE-TIME:20231023T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20231016T150000Z
DTEND;VALUE=DATE-TIME:20231016T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20231113T150000Z
DTEND;VALUE=DATE-TIME:20231113T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20231127T150000Z
DTEND;VALUE=DATE-TIME:20231127T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20231106T150000Z
DTEND;VALUE=DATE-TIME:20231106T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20231120T150000Z
DTEND;VALUE=DATE-TIME:20231120T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20231204T150000Z
DTEND;VALUE=DATE-TIME:20231204T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20231211T150000Z
DTEND;VALUE=DATE-TIME:20231211T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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 R. López-Permouth (Ohio University\, USA)
DTSTART;VALUE=DATE-TIME:20240108T150000Z
DTEND;VALUE=DATE-TIME:20240108T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/51
DESCRIPTION:Title: B
asic Extension Modules (All bases are created equal\, but some are more eq
ual than others)\nby Sergio R. López-Permouth (Ohio University\, USA)
as part of European Non-Associative Algebra Seminar\n\n\nAbstract\nWe rep
ort on ongoing research about a module-theoretic construction which\, when
successful\, yields natural extensions of infinite dimensional modules ov
er arbitrary algebras. Whether the construction works or not depends on th
e basis 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
done so far has focused on infinite dimensional algebra of polynomials on
a single variable. We will see that amenability and related notions serve
to classify the distinct bases according to interesting complementary prop
erties having to do with the types of relations induced on them by the pro
perties 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;VALUE=DATE-TIME:20240115T150000Z
DTEND;VALUE=DATE-TIME:20240115T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240122T150000Z
DTEND;VALUE=DATE-TIME:20240122T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240129T150000Z
DTEND;VALUE=DATE-TIME:20240129T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240205T150000Z
DTEND;VALUE=DATE-TIME:20240205T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240212T150000Z
DTEND;VALUE=DATE-TIME:20240212T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240219T150000Z
DTEND;VALUE=DATE-TIME:20240219T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240226T150000Z
DTEND;VALUE=DATE-TIME:20240226T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240304T150000Z
DTEND;VALUE=DATE-TIME:20240304T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240311T150000Z
DTEND;VALUE=DATE-TIME:20240311T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240325T150000Z
DTEND;VALUE=DATE-TIME:20240325T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240408T150000Z
DTEND;VALUE=DATE-TIME:20240408T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240415T150000Z
DTEND;VALUE=DATE-TIME:20240415T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240422T150000Z
DTEND;VALUE=DATE-TIME:20240422T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240506T150000Z
DTEND;VALUE=DATE-TIME:20240506T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240318T150000Z
DTEND;VALUE=DATE-TIME:20240318T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240520T150000Z
DTEND;VALUE=DATE-TIME:20240520T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240624T150000Z
DTEND;VALUE=DATE-TIME:20240624T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240527T150000Z
DTEND;VALUE=DATE-TIME:20240527T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240603T150000Z
DTEND;VALUE=DATE-TIME:20240603T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240610T150000Z
DTEND;VALUE=DATE-TIME:20240610T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240617T150000Z
DTEND;VALUE=DATE-TIME:20240617T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240401T150000Z
DTEND;VALUE=DATE-TIME:20240401T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240429T150000Z
DTEND;VALUE=DATE-TIME:20240429T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240701T150000Z
DTEND;VALUE=DATE-TIME:20240701T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240715T150000Z
DTEND;VALUE=DATE-TIME:20240715T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240722T150000Z
DTEND;VALUE=DATE-TIME:20240722T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240812T150000Z
DTEND;VALUE=DATE-TIME:20240812T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240902T150000Z
DTEND;VALUE=DATE-TIME:20240902T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240513T150000Z
DTEND;VALUE=DATE-TIME:20240513T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240909T150000Z
DTEND;VALUE=DATE-TIME:20240909T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240729T150000Z
DTEND;VALUE=DATE-TIME:20240729T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240819T150000Z
DTEND;VALUE=DATE-TIME:20240819T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240826T150000Z
DTEND;VALUE=DATE-TIME:20240826T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20241007T150000Z
DTEND;VALUE=DATE-TIME:20241007T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240916T150000Z
DTEND;VALUE=DATE-TIME:20240916T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240930T150000Z
DTEND;VALUE=DATE-TIME:20240930T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240805T150000Z
DTEND;VALUE=DATE-TIME:20240805T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20240708T150000Z
DTEND;VALUE=DATE-TIME:20240708T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20241021T150000Z
DTEND;VALUE=DATE-TIME:20241021T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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\nInter
active livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract\nIn th
is talk\, I will discuss a general method to renormalise singular stochast
ic partial differential equations (SPDEs) using the theory of regularity s
tructures. It turns out that\, to derive the renormalised equation\, one c
an employ a convenient multi-pre-Lie algebra. The pre-Lie products in this
algebra are reminiscent of the pre-Lie product on the Grossman-Larson alg
ebra of trees\, but come with several important twists. For the renormalis
ation of SPDEs\, the important feature of this multi-pre-Lie algebra is th
at it is free in a certain sense. Based on joint work with Yvain Bruned\,
Ajay Chandra\, and Martin Hairer.\n
LOCATION:https://researchseminars.org/talk/ENAAS/94/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carla Rizzo (University of Palermo\, Italy)
DTSTART;VALUE=DATE-TIME:20241111T150000Z
DTEND;VALUE=DATE-TIME:20241111T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/95
DESCRIPTION:Title: G
eneralized polynomial identities\nby Carla Rizzo (University of Palerm
o\, Italy) as part of European Non-Associative Algebra Seminar\n\nInteract
ive livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract\nA genera
lized polynomial identity of an algebra A over a field F is a polynomial e
xpression in non-commutative variables and fixed coefficients from A betwe
en the variables such that vanishes upon all substitutions by elements of
A. It is a natural extension of the notion of a polynomial identity\, in w
hich the coefficients come from the base field F. The idea of generalized
polynomial identities stems from the observation that sometimes when we st
udy polynomials in matrix algebras\, we want to focus on evaluations where
certain variables are always replaced by specific elements. The purpose o
f this talk is to present some recent results on the descrip- tion of gene
ralized polynomial identities of some interesting algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/95/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Fernández (Technical University of Madrid\, Spain)
DTSTART;VALUE=DATE-TIME:20241202T150000Z
DTEND;VALUE=DATE-TIME:20241202T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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\nInteractive livestream: https://us02web.zo
om.us/j/7803181064\n\nAbstract\nIn order to define suitable noncommutative
Poisson structures\, M. Van den Bergh introduced double Poisson algebras
and double quasi-Poisson algebras. Furthermore\, N. Iyudu and M. Kontsevic
h found an insightful correspondence between double Poisson algebras and p
re-Calabi-Yau algebras\; certain cyclic A∞-algebras which can be seen as
noncommutative versions of shifted Poisson manifolds. In this talk I will
present an extension of the Iyudu-Kontsevich correspondence to the differ
ential graded setting. I will also explain how double quasi-Poisson algebr
as give rise to pre-Calabi-Yau algebras. This is a joint work with E. Hers
covich (EPFL).\n
LOCATION:https://researchseminars.org/talk/ENAAS/96/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alicia Tocino Sánchez (University of Málaga\, Spain)
DTSTART;VALUE=DATE-TIME:20241216T150000Z
DTEND;VALUE=DATE-TIME:20241216T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n\nAbst
ract\nThe starting point of this talk is the fact that the class of evolut
ion algebras over a fixed field is closed under tensor product. We prove t
hat\, under certain conditions\, the tensor product is an evolution algebr
a if and only if every factor is an evolution algebra. Another issue arise
s about the inheritance of properties from the tensor product to the facto
rs and conversely. For instance\, nondegeneracy\, irreducibility\, perfect
ness and simplicity are investigated. The four-dimensional case is illustr
ative and useful to contrast conjectures\, so we achieve a complete classi
fication of four-dimensional perfect evolution algebras emerging as tensor
product of two-dimensional ones. We find that there are four-dimensional
evolution algebras that are the tensor product of two nonevolution algebra
s. This is a joint work together with Yolanda Cabrera Casado\, Dolores Mar
tín Barquero and Cándido Martín González.\n
LOCATION:https://researchseminars.org/talk/ENAAS/97/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Raschid Abedin (ETH Zürich\, Switzerland)
DTSTART;VALUE=DATE-TIME:20241028T150000Z
DTEND;VALUE=DATE-TIME:20241028T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n\
nAbstract\nIn a now classic paper\, Belavin and Drinfeld categorized solut
ions to the classical Yang-Baxter equation (CYBE)\, an equation crucial to
the theory of integrable systems\, into three classes: elliptic\, trigono
metric and rational. It is possible to reproduce this result by geometrizi
ng solutions of the CYBE and then applying algebro-geometric methods. In t
his talk\, we will explain how this approach can be used to categorize Lie
bialgebra structures on power series Lie algebras\, as well as non-associ
ative generalizations of these structures: D-bialgebra structures on more
general power series algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/98/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Omar León Sánchez (University of Manchester\, UK)
DTSTART;VALUE=DATE-TIME:20241209T150000Z
DTEND;VALUE=DATE-TIME:20241209T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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\nInteractive livestream: h
ttps://us02web.zoom.us/j/7803181064\n\nAbstract\nI will present joint work
with Sue Sierra where we proved the ACC for radical Poisson ideals of the
symmetric algebra of a Dicksonian Lie algebra. Part of the talk will be d
evoted to explaining what Dicksonian means (and give a variety of examples
)\, and then discuss the method of proof of the basis theorem. We will obs
erve why our result applies to graded-simple Lie algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/99/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Slaven Kožić (University of Zagreb\, Croatia)
DTSTART;VALUE=DATE-TIME:20241014T150000Z
DTEND;VALUE=DATE-TIME:20241014T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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
Interactive livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract\n
One important problem in the vertex algebra theory is to associate certai
n vertex algebra-like objects\, the quantum vertex algebras\, to\nvariou
s classes of quantum groups\, such as quantum affine algebras or double Ya
ngians.\nIn this talk\, I will discuss this problem in the context of
Etingof--Kazhdan's quantum affine vertex algebra $\\mathcal{V}^c(\\mathfr
ak{gl}_N)$ associated with the trigonometric $R$-matrix of type $A$. \nTh
e main focus will be on the explicit description of the center of $\\math
cal{V}^c(\\mathfrak{gl}_N)$ 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 affine algebra
of type $A$ and the orthogonal twisted $h$-Yangian. The talk is in part b
ased on the joint works with Alexander Molev and Lucia Bagnoli.\n
LOCATION:https://researchseminars.org/talk/ENAAS/100/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ignacio Bajo (University of Vigo\, Spain)
DTSTART;VALUE=DATE-TIME:20240923T150000Z
DTEND;VALUE=DATE-TIME:20240923T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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;VALUE=DATE-TIME:20241104T150000Z
DTEND;VALUE=DATE-TIME:20241104T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/102
DESCRIPTION:Title:
Pairs of quotients of Jordan pairs vialocalorders\nby Fernando Montane
r (University of Zaragoza\, Spain) as part of European Non-Associative Alg
ebra Seminar\n\nInteractive livestream: https://us02web.zoom.us/j/78031810
64\n\nAbstract\nIn this talk we expose ongoing joint work with I Paniello
on systems of quotients (in a sense partially extending the localization t
heory of Jordan algebras\, which in turn is inspired by the localization t
heory of associative algebras). Localization theory in associative algebra
s originated in the purpose of extending the construction of fields of quo
tients of integral domains\, and therefore in the purpose of defining rin
g extensions in which a selected set of elements become invertible. As it
is well known in associative theory that led to Goldie's theorems\, and t
hese in turn to more general localization theories for which the denominat
ors of the fraction-like elements of the extensions are (one-sided) ideals
taken in a class of filters (Gabriel filters). These ideas have been part
ially extended to Jordan algebras by several authors (starting with Zelman
ov's version of Goldie theory in the Jordan setting\, and its extension by
Fernandez López-García Rus and Montaner) and Paniello and Montaner (amo
ng others) definition of algebras of quotients of Jordan algebras. Followi
ng the development of Jordan theory\, a natural direction for extending th
ese results is considering the context of Jordan pairs. This is the object
ive of the research presented here. Since obviously a Jordan pair cannot h
ave invertible elements unless it is an algebra\, and in this case we are
back in the already developed theory\, the kind of quotients that would ma
ke a significative (proper) extension of the case of algebras should be ba
sed in a different notion of quotient. An approach that seems to be promi
sing is considering the Jordan extension of Fountain and Gould notion of l
ocal order\, as has been adapted to Jordan algebras by the work of Fernán
dez López\, and more recently by Montaner and Paniello with the notion of
local order\, in which the bridge between algebras and pairs is establish
ed by local algebras following the ideas of D'Amour and McCrimmon. In the
talk 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/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Carlos André (University of Lisboa\, Portugal)
DTSTART;VALUE=DATE-TIME:20241125T150000Z
DTEND;VALUE=DATE-TIME:20241125T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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\nInteractive livestream: https://us02we
b.zoom.us/j/7803181064\n\nAbstract\nDescribing the conjugacy classes and/o
r irreducible characters of the unitriangular group over a finite field is
known to be an impossibly difficult problem. Superclasses and supercharac
ters have been introduced (under the names of "basic varieties" and "basic
characters") as an attempt to approximate conjugacy classes and irreducib
le characters using a cruder version of Kirillov's method of coadjoint orb
its.\n\nIn the past thirty years\, these notions have been recognised in s
everal areas (seemingly unrelated to representation theory): exponential s
ums in number theory\, random walks in probability and statistics\, associ
ation schemes in algebraic combinatorics...\n\nIn this talk\, we will desc
ribe 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 factorisation
of supercharacters of unitriangular groups which explains the alternative
definition as basic characters.\n
LOCATION:https://researchseminars.org/talk/ENAAS/103/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pablo Zadunaisky (University of Buenos Aires\, Argentina)
DTSTART;VALUE=DATE-TIME:20241118T150000Z
DTEND;VALUE=DATE-TIME:20241118T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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\nIn
teractive livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract\nBy
an ultra classical result\, the tensor product of a simple representation
of gl(n\,C) and its defining representation decomposes as a direct sum of
simple representations without multiplicities. This means that for each h
ighest weight\, the space of highest weight vectors is one dimensional. We
will give an explicit construction of these highest weight vectors\, and
show that they arise from the action of certain elements in the enveloping
algebra of gl(n\,c)+gl(n\,C) on the tensor product. These elements are in
dependent of the simple representation we started with\, and in fact produ
ce highest weight vectors in several other contexts. (Joint with Joanna Me
inel from Bonn University)\n
LOCATION:https://researchseminars.org/talk/ENAAS/104/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Stewart (University of Manchester\, UK)
DTSTART;VALUE=DATE-TIME:20250106T150000Z
DTEND;VALUE=DATE-TIME:20250106T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n
\nAbstract\nLet k be a field\, let G be a smooth affine k-group 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 each indecomposa
ble summand of V \; say V is geometrically rigid (resp. absolutely rigid )
if V is rigid after base change of G and V to an algebraic closure of k (
resp. any field extension of k). We show that all simple G-modules are geo
metrically rigid\, though they are not in general absolutely rigid. More p
recisley\, 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 such that V_{
k_V} is absolutely rigid as a G_{k_V} -module. The proof for connected G t
urns on an investigation of algebras of the form K \\otimes_k E where K an
d E are field extensions of k\; we give an example of such an algebra whic
h is not rigid as a module over itself. We establish the existence of the
purely inseparable field extension k_V /k through an analogous version for
artinian algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/105/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dmitry Millionshchikov (Lomonosov University\, Russia)
DTSTART;VALUE=DATE-TIME:20250113T150000Z
DTEND;VALUE=DATE-TIME:20250113T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/106
DESCRIPTION:Title:
Narrow N-graded Lie (super)algebras\nby Dmitry Millionshchikov (Lomono
sov University\, Russia) as part of European Non-Associative Algebra Semin
ar\n\nInteractive livestream: https://us02web.zoom.us/j/7803181064\nAbstra
ct: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/106/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Mancini (University of Palermo\, Italy)
DTSTART;VALUE=DATE-TIME:20250120T150000Z
DTEND;VALUE=DATE-TIME:20250120T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/107
DESCRIPTION:by Manuel Mancini (University of Palermo\, Italy) as part of E
uropean Non-Associative Algebra Seminar\n\nInteractive livestream: https:/
/us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/107/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Roman Stasenko (HSE University\, Russia)
DTSTART;VALUE=DATE-TIME:20250127T150000Z
DTEND;VALUE=DATE-TIME:20250127T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
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\nInteractive livestream: https://us02web.zoom.us/j/780
3181064\n\nAbstract\nLet $S$ be an arbitrary reductive algebraic group. Le
t's call a homomorphism $\\Phi:S\\rightarrow\\operatorname{Aut}(\\mathfra
k{g})$ an {\\it $S$-structure on the Lie algebra $\\mathfrak{g}$}. $S$-str
uctures were previously invetigated by various authors\, including E.B. Vi
nberg. The talk deals with $SL_2$-structures. Let's call the $SL_2$-struct
ure short if the representation $\\Phi$ of the group $SL_2$ decomposes int
o irreducible representations of dimensions 1\, 2 and 3. If we consider ir
reducible representations of dimensions only 1 and 3\, we get the well-kno
wn Tits-Kantor-Koeher construction\, which establishes a one-to-one corres
pondence between simple Jordan algebras and simple Lie algebras of a certa
in type. Similarly to the Tits–Kantor–Koeher theorem\, in the case of
short $SL_2$-structures\, there is a one-to-one correspondence between si
mple Lie algebras with such a structure and the so-called simple symplecti
c Lie-Jordan structures. Let $\\mathfrak{g}$ be a Lie algebra with $SL_2$
-structure and the map $\\rho:\\mathfrak{g}\\rightarrow\\mathfrak{gl}(U)$
be linear representation of $\\mathfrak{g}$. The homophism $\\Psi:S\\right
arrow GL(U)$ is called a $SL_2$-structure on the Lie $\\mathfrak{g}$-modul
e $U$ if $$\\Psi(s)\\rho(\\xi)u =\\rho(\\Phi(s)\\xi)\\Psi(s)u\,\\quad\\for
all s\\in S\, \\xi\\in\\mathfrak{g}\, u\\in U.$$ This constrution has inte
resting applications to the representation theory of Jordan algebras\, whi
ch will be discussed during the talk. We will also present a complete clas
sification of irreducible short $\\mathfrak{g}$-modules for simple Lie alg
ebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/108/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lina Oliveira (IST University of Lisboa\, Portugal)
DTSTART;VALUE=DATE-TIME:20250203T150000Z
DTEND;VALUE=DATE-TIME:20250203T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/109
DESCRIPTION:by Lina Oliveira (IST University of Lisboa\, Portugal) 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/109/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrea Sciandra (University of Turin\, Italy)
DTSTART;VALUE=DATE-TIME:20250210T150000Z
DTEND;VALUE=DATE-TIME:20250210T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/110
DESCRIPTION:by Andrea Sciandra (University of Turin\, Italy) as part of Eu
ropean Non-Associative Algebra Seminar\n\nInteractive livestream: https://
us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/110/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Guy Blachar (Bar-Ilan University\, Israel)
DTSTART;VALUE=DATE-TIME:20250217T150000Z
DTEND;VALUE=DATE-TIME:20250217T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/111
DESCRIPTION:by Guy Blachar (Bar-Ilan University\, Israel) as part of Europ
ean Non-Associative Algebra Seminar\n\nInteractive livestream: https://us0
2web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/111/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Leandro Vendramin (Free University of Brussels\, Belgium)
DTSTART;VALUE=DATE-TIME:20250224T150000Z
DTEND;VALUE=DATE-TIME:20250224T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/112
DESCRIPTION:by Leandro Vendramin (Free University of Brussels\, Belgium) a
s part of European Non-Associative Algebra Seminar\n\nInteractive livestre
am: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/112/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Loïc Foissy (University of the Littoral Opal Coast\, France)
DTSTART;VALUE=DATE-TIME:20250303T150000Z
DTEND;VALUE=DATE-TIME:20250303T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/113
DESCRIPTION:by Loïc Foissy (University of the Littoral Opal Coast\, Franc
e) as part of European Non-Associative Algebra Seminar\n\nInteractive live
stream: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/113/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anna Fino (University of Turin\, Italy)
DTSTART;VALUE=DATE-TIME:20250317T150000Z
DTEND;VALUE=DATE-TIME:20250317T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/114
DESCRIPTION:by Anna Fino (University of Turin\, Italy) as part of European
Non-Associative Algebra Seminar\n\nInteractive livestream: https://us02we
b.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/114/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bruno Vallette (Sorbonne Paris North University\, France)
DTSTART;VALUE=DATE-TIME:20250324T150000Z
DTEND;VALUE=DATE-TIME:20250324T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/115
DESCRIPTION:by Bruno Vallette (Sorbonne Paris North University\, France) a
s part of European Non-Associative Algebra Seminar\n\nInteractive livestre
am: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/115/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bernhard Keller (Paris Cité University\, France)
DTSTART;VALUE=DATE-TIME:20250331T150000Z
DTEND;VALUE=DATE-TIME:20250331T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/116
DESCRIPTION:by Bernhard Keller (Paris Cité University\, France) as part o
f European Non-Associative Algebra Seminar\n\nInteractive livestream: http
s://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/116/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jari Desmet (Ghent University\, Belgium)
DTSTART;VALUE=DATE-TIME:20250407T150000Z
DTEND;VALUE=DATE-TIME:20250407T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/117
DESCRIPTION:by Jari Desmet (Ghent University\, Belgium) 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/117/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kailash Misra (North Carolina State University\, USA)
DTSTART;VALUE=DATE-TIME:20250310T150000Z
DTEND;VALUE=DATE-TIME:20250310T160000Z
DTSTAMP;VALUE=DATE-TIME:20241013T144435Z
UID:ENAAS/118
DESCRIPTION:by Kailash Misra (North Carolina State University\, USA) as pa
rt of European Non-Associative Algebra Seminar\n\nInteractive livestream:
https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/118/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
END:VCALENDAR