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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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
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\nInte
ractive livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract\nThe
title matches that of a series of papers by various authors beginning in 1
997\, whose goal was the study and classification of such algebras over fi
elds of positive characteristic. The original motivation came from group t
heory: the Leedham-Green and Newman coclass conjectures on pro-p groups fr
om 1980 had all become theorems relatively recently\, and subsequent resul
ts of Shalev and Zelmanov had raised interest in what one could say about
Lie algebras of finite coclass. In positive characteristic\, the simplest
case of coclass one (i.e.\, 'Lie algebras of maximal class'\, also called
'filiform' in some quarters) appeared challenging even under the strong as
sumptions of those Lie algebras being infinite-dimensional and graded over
the positive integers. I will review motivations and results of those stu
dies\, including some classifications obtained by Caranti\, Newman\, Vaugh
an-Lee. Then I will describe some generalizations recently established wit
h three of my former PhD students.\n
LOCATION:https://researchseminars.org/talk/ENAAS/23/
URL:https://us02web.zoom.us/j/7803181064
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:20230610T191043Z
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\nInteractive livestream: https://us02web.zoom.us/j/7803181064\n\nA
bstract\nWe say that an element $x$ in a ring $R$ is nilpotent last-regula
r if it is nilpotent of certain index $n+1$ and its last nonzero power $x^
n$ is regular von Neumann\, i.e.\, there exists another element $y\\in R$
such that $x^nyx^n=x^n$. This type of elements naturally arise when studyi
ng 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 m
oving to the symmetric Martindale ring of quotients $Q^s_m(R)$ of $R$ we s
till obtain inner derivations with the same indices of nilpotence 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 nilpotent last-r
egular element. This condition strongly determines the structure of $Q^s_m
(R)$ and of $\\Skew(Q^s_m(R)\,*)$. \nWe will review the Jordan canonical f
orm of nilpotent last-regular elements and show how to get gradings in ass
ociative algebras (with and without involution) when they have such elemen
ts.\n
LOCATION:https://researchseminars.org/talk/ENAAS/24/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sigiswald Barbier (Ghent University\, Belgium)
DTSTART;VALUE=DATE-TIME:20230703T150000Z
DTEND;VALUE=DATE-TIME:20230703T160000Z
DTSTAMP;VALUE=DATE-TIME:20230610T191043Z
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\nInter
active livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract\nDiagr
am categories are a special kind of tensor categories that can be represen
ted using diagrams. In this talk I will give an introduction to categories
represented using Brauer diagrams. In particular I will explain the relat
ion with the Brauer algebra and how the categorical framework can be appli
ed to representation theory of the corresponding algebra.\n
LOCATION:https://researchseminars.org/talk/ENAAS/25/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ivan Arzhantsev (HSE University\, Russia)
DTSTART;VALUE=DATE-TIME:20230515T150000Z
DTEND;VALUE=DATE-TIME:20230515T160000Z
DTSTAMP;VALUE=DATE-TIME:20230610T191043Z
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:20230610T191043Z
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:20230610T191043Z
UID:ENAAS/28
DESCRIPTION:by Csaba Schneider (Federal University of Minas Gerais\, Brazi
l) 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/28/
URL:https://us02web.zoom.us/j/7803181064
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:20230610T191043Z
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\nInteractive livestrea
m: https://us02web.zoom.us/j/7803181064\n\nAbstract\nI will present the fi
rst notions concerning heaps and trusses. Heaps were introduced for the fi
rst time by H. Prüfer (1924) and R. Baer (1929). A heap is a pair $(H\,
[−\,−\,−])$ consisting of a set $H$ and a ternary operation $$[−\,
−\,−] : H \\times H \\times H \\to H\, (x\, y\, z) \\to [x\, y\, z]
\,$$ 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. Brzeziński\, 20
19). A truss is a heap with a further associative binary operation\, denot
ed 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/
URL:https://us02web.zoom.us/j/7803181064
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:20230610T191043Z
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\nIntera
ctive livestream: https://us02web.zoom.us/j/7803181064\n\nAbstract\nLet $K
\\langle X\\rangle$ denote the free associative algebra generated by a fin
ite set $X$ with n elements over a field $K$ of characteristic 0. Let $I_p
$ denote the two-sided associative ideal in $K\\langle X\\rangle$ generate
d by all commutators of length $p$\, where $p$ is an arbitrary positive in
teger greater than 1. The group ${\\rm GL(n)}$ acts in a natural way on th
e quotient $K\\langle X\\rangle/I_p$ and the ${\\rm GL(n)}$-module structu
re of $K\\langle X\\rangle/I_p$ is known for $p=2\,3\,4\,5$. In this talk\
, we give some results on the ${\\rm GL}(n)$-module structure of $K\\langl
e X\\rangle/I_p$ for any $p$. More precisely\, we give a bound on the valu
es of the highest weights of irreducible ${\\rm GL}(n)$-modules which appe
ar in the decomposition of $K\\langle X\\rangle/I_p$. We discuss also appl
ications of these results related to the algebras of G-invariants in $K\\l
angle X\\rangle/I_p$\, where G is one of the classical ${\\rm GL}(n)$-subg
roups ${\\rm SL}(n)$\, ${\\rm O}(n)$\, ${\\rm SO}(n)$\, or ${\\rm Sp}(2k)$
(for $n=2k$).\n
LOCATION:https://researchseminars.org/talk/ENAAS/30/
URL:https://us02web.zoom.us/j/7803181064
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:20230610T191043Z
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\nInteractive livestream: https://us02web.zoom.us/j/7803
181064\n\nAbstract\nIn this talk we will present recent results on the cat
egory of finite-dimensional modules for map superalgebras. Firstly\, we wi
ll show a new description of certain irreducible modules. Secondly\, we wi
ll use this new description to extract homological properties of the categ
ory of finite-dimensional modules for map superalgebras\, most importantly
\, its block decomposition.\n
LOCATION:https://researchseminars.org/talk/ENAAS/31/
URL:https://us02web.zoom.us/j/7803181064
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:20230610T191043Z
UID:ENAAS/32
DESCRIPTION:by Andrea Solotar (University of Buenos Aires\, Argentina) as
part of European Non-Associative Algebra Seminar\n\nInteractive livestream
: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/32/
URL:https://us02web.zoom.us/j/7803181064
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:20230610T191043Z
UID:ENAAS/33
DESCRIPTION:by Alexey Petukhov (Institute for Information Transmission Pro
blems\, Russia) as part of European Non-Associative Algebra Seminar\n\nInt
eractive livestream: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/33/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Şehmus Fındık (Çukurova University\, Turkey)
DTSTART;VALUE=DATE-TIME:20230731T150000Z
DTEND;VALUE=DATE-TIME:20230731T160000Z
DTSTAMP;VALUE=DATE-TIME:20230610T191043Z
UID:ENAAS/34
DESCRIPTION:by Şehmus Fındık (Çukurova University\, Turkey) as part of
European Non-Associative Algebra Seminar\n\nInteractive livestream: https
://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/34/
URL:https://us02web.zoom.us/j/7803181064
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:20230610T191043Z
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\nInteractive livestream: https://us02web.zoom.us/j/
7803181064\n\nAbstract\nStable equivalences occur frequently in the repres
entation theory of finite-dimensional algebras\; however\, these equivalen
ces are poorly understood. An interesting class of stable equivalences is
obtained by ‘gluing’ two idempotents. More precisely\, let A be a fini
te-dimensional algebra with a simple projective module and a simple inject
ive module. Assume that B is a subalgebra of A having the same Jacobson ra
dical. Then B is constructed by identifying the two idempotents belonging
to the simple projective module and to the simple injective module\, respe
ctively. \n\nIn this talk\, we will compare the first Hochschild cohomolog
y groups of finite-dimensional monomial algebras under gluing two arbitrar
y idempotents (hence not necessarily inducing a stable equivalence). As a
corollary\, we will show that stable equivalences obtained by gluing two i
dempotents provide 'some functoriality' to the first Hochschild cohomology
\, that is\, HH^1(A) is isomorphic to a quotient of HH^1(B).\n
LOCATION:https://researchseminars.org/talk/ENAAS/35/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Joscha Diehl (University of Greifswald\, Germany)
DTSTART;VALUE=DATE-TIME:20230904T150000Z
DTEND;VALUE=DATE-TIME:20230904T160000Z
DTSTAMP;VALUE=DATE-TIME:20230610T191043Z
UID:ENAAS/36
DESCRIPTION:by Joscha Diehl (University of Greifswald\, Germany) 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/36/
URL:https://us02web.zoom.us/j/7803181064
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:20230610T191043Z
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\nInteractive livestream: https://us02web.zoom.us/j/78
03181064\n\nAbstract\nWe describe the defining identities of a variety of
binary perm algebras which is a subvariety of the variety of alternative a
lgebras. Moreover\, we construct a basis of the free binary perm algebra.
In addition\, we describe the subalgebras of binary perm algebras under co
mmutator which has a connection with Malcev algebras.\n
LOCATION:https://researchseminars.org/talk/ENAAS/37/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hader Elgendy (Damietta University\, Egypt)
DTSTART;VALUE=DATE-TIME:20230925T150000Z
DTEND;VALUE=DATE-TIME:20230925T160000Z
DTSTAMP;VALUE=DATE-TIME:20230610T191043Z
UID:ENAAS/38
DESCRIPTION:by Hader Elgendy (Damietta University\, Egypt) as part of Euro
pean Non-Associative Algebra Seminar\n\nInteractive livestream: https://us
02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/38/
URL:https://us02web.zoom.us/j/7803181064
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:20230610T191043Z
UID:ENAAS/39
DESCRIPTION:by Alfilgen Sebandal (Mindanao State University\, Philippines)
as part of European Non-Associative Algebra Seminar\n\nInteractive livest
ream: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/39/
URL:https://us02web.zoom.us/j/7803181064
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:20230610T191043Z
UID:ENAAS/40
DESCRIPTION:by Adam Chapman (Academic College of Tel-Aviv-Yaffo\, Israel)
as part of European Non-Associative Algebra Seminar\n\nInteractive livestr
eam: https://us02web.zoom.us/j/7803181064\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/ENAAS/40/
URL:https://us02web.zoom.us/j/7803181064
END:VEVENT
END:VCALENDAR