BEGIN:VCALENDAR
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BEGIN:VEVENT
SUMMARY:Zerui Zhang (South China Normal University\, China)
DTSTART:20221226T080000Z
DTEND:20221226T090000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/1
DESCRIPTION:Title: Some results on Novikov algebras and Novikov-Poisson algebras\nby Zerui Zhang (South China Normal University\, China) as part of Non-A
ssociative Day in Online\n\n\nAbstract\nWe first prove that a left Novikov
algebra is right nilpotent if and only if it is solvable. And we show tha
t the ideal generated by all the commutators of a Lie nilpotent Novikov al
gebra is nilpotent. Then a connection between Novikov algebras and differe
ntial commutative algebras will be discussed. Finally\, we show that such
a connection have an analogue between unital Novikov-Poisson algebras and
special Novikov-Poisson admissible algebras.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jiefeng Liu (Northeast Normal University\, China)
DTSTART:20221226T090000Z
DTEND:20221226T100000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/2
DESCRIPTION:Title: Cohomology and deformation quantization of Poisson conformal alg
ebras\nby Jiefeng Liu (Northeast Normal University\, China) as part of
Non-Associative Day in Online\n\n\nAbstract\nIn this talk\, we first reca
ll the notion of (noncommutative) Poisson conformal algebras and give some
constructions of them. Then we introduce the notion of conformal formal d
eformations of commutative associative conformal algebras and show that Po
isson conformal algebras are the corresponding semi-classical limits. At l
ast\, we develop the cohomology theory of noncommutative Poisson conformal
algebras and use this cohomology to study their deformations.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chengming Bai (Nankai University\, China)
DTSTART:20221226T100000Z
DTEND:20221226T110000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/3
DESCRIPTION:Title: Parity duality of super r-matrices via O-operators and pre-Lie s
uperalgebras\nby Chengming Bai (Nankai University\, China) as part of
Non-Associative Day in Online\n\n\nAbstract\nWe interpret the homogeneous
solutions of the super classical Yang-Baxter equation\, also called super
r-matrices\, in terms of O-operators by a unified treatment. Furthermore\,
by a parity reversion of Lie superalgebra representations\, a duality is
established between the even and odd O-operators. This leads to a parity d
uality of the super r-matrices induced by the O-operators in semi-direct p
roduct Lie superalgebras. Therefore a pre-Lie superalgebra naturally defin
es an even O-operator\, and hence an odd O-operator by the duality\, there
by giving rise to a parity pair of super r-matrices. This is a joint work
with Li Guo and Runxuan Zhang.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xiangui Zhao (Huizhou University\, China)
DTSTART:20221226T120000Z
DTEND:20221226T130000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/4
DESCRIPTION:Title: Growth and Gelfand-Kirillov dimension of brace algebras\nby
Xiangui Zhao (Huizhou University\, China) as part of Non-Associative Day i
n Online\n\n\nAbstract\nA brace algebra over a field is a vector space equ
ipped with a family of linear operations satisfying certain identities. Br
ace algebras have strong connections with other important classes of algeb
ras such as pre-Lie algebras\, ε-bialgebras\, and dendriform algebras. Th
e Gelfand-Kirillov dimension of a (not necessarily associative) algebra is
an important invariant for the study of the growth of the algebra. In thi
s talk\, we discuss the growth and possible values of the Gelfand-Kirillov
dimension of brace algebras. In particular\, we construct examples to sho
w that the Bergman's gap theorem for the Gelfand-Kirillov dimension of ass
ociative algebras does not hold for brace algebras. This is joint work wit
h Qiuhui Mo\, Yu Li\, and Wenchao Zhang.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Farkhod Eshmatov (AKFA University\, Uzbekistan)
DTSTART:20221226T130000Z
DTEND:20221226T140000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/5
DESCRIPTION:Title: Necklace Lie algebra and derived Poisson structure\nby Farkh
od Eshmatov (AKFA University\, Uzbekistan) as part of Non-Associative Day
in Online\n\n\nAbstract\nWe introduce the notion of a derived Poisson stru
cture on an associative (not necessarily commutative) algebra. Then we wil
l discuss how Necklace Lie algebra structure can be used to construct deri
ved Poisson bracket for some interesting classes of algebras.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uzi Vishne (Bar Ilan University\, Israel)
DTSTART:20221226T140000Z
DTEND:20221226T150000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/6
DESCRIPTION:Title: Identities of the tensor square of the octonion algebra\nby
Uzi Vishne (Bar Ilan University\, Israel) as part of Non-Associative Day i
n Online\n\n\nAbstract\nWe describe the nonassociative polynomial identiti
es of minimal degree\, which is 7\, for the algebras $\\mathcal O \\times
\\mathcal O$ and ${\\rm M}_2(\\mathcal O)\,$ where $\\mathcal O$ is the oc
tonion algebra. After being discovered by a computer\, the proofs are rath
er elegant. We also discuss some related open problems on varieties of non
associative algebras.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniel Fox (Polytechnic University of Madrid\, Spain)
DTSTART:20221226T160000Z
DTEND:20221226T170000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/7
DESCRIPTION:Title: Sectional nonassociativity of metrized algebras\nby Daniel F
ox (Polytechnic University of Madrid\, Spain) as part of Non-Associative D
ay in Online\n\n\nAbstract\nThe sectional nonassociativity of a metrized (
not necessarily associative or unital) algebra is defined analogously to t
he sectional curvature of a pseudo-Riemannian metric\, with the associator
in place of the Levi-Civita covariant derivative. For commutative real al
gebras nonnegative sectional nonassociativity is usually called the Norton
inequality\, while a sharp upper bound on the sectional nonassociativity
of the Jordan algebra of Hermitian matrices over a real Hurwitz algebra is
closely related to what is known as the Böttcher-Wenzel-Chern-do Carmo-K
obayashi inequality. These and other basic examples are explained\, and th
ere are described some consequences of bounds on sectional nonassociativit
y for commutative algebras.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Xingting Wang (Howard University\, USA)
DTSTART:20221226T170000Z
DTEND:20221226T180000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/8
DESCRIPTION:Title: Twisting of graded quantum groups and solutions to the quantum Y
ang-Baxter equation\nby Xingting Wang (Howard University\, USA) as par
t of Non-Associative Day in Online\n\n\nAbstract\nLet $H$ be a Hopf algebr
a over a field $k$ such that $H$ is $\\mathbb Z$-graded as an algebra. In
this talk\, we introduce the notion of a twisting pair for $H$ and show th
at the Zhang twist of $H$ by such a pair can be realized as a $2$-cocycle
twist. We use twisting pairs to describe twists of Manin’s universal qua
ntum groups associated to quadratic algebras. Furthermore\, we discuss a s
trategy to twist a solution to the quantum Yang-Baxter equation via the Fa
ddeev-Reshetikhin-Takhtajan construction. If time permits\, we illustrate
this result for the quantized coordinate rings of ${\\rm GL}_n(k)$. This i
s joint work with Hongdi Huang\, Van Nguyen\, Charlotte Ure\, Kent Vashaw
and Padmini Veerapen.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Li Guo (Rutgers University\, USA)
DTSTART:20221226T180000Z
DTEND:20221226T190000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/9
DESCRIPTION:Title: Coherent categorical structures for Lie bialgebras\, Manin tripl
es\, classical r-matrices and pre-Lie algebras\nby Li Guo (Rutgers Uni
versity\, USA) as part of Non-Associative Day in Online\n\n\nAbstract\nThe
broadly applied notions of Lie bialgebras\, Manin triples\, classical r-m
atrices and O-operators of Lie algebras owe their importance to the close
relationship among them. Yet these notions and their correspondences are m
ostly understood as classes of objects and maps among the classes. To gain
categorical insight\, we introduce\, for each of the classes\, a notion o
f homomorphisms\, uniformly called coherent homomorphisms\, so that the cl
asses of objects become categories and the maps among the classes become f
unctors or category equivalences. For this purpose\, we start with the not
ion of an endo Lie algebra\, consisting of a Lie algebra equipped with a L
ie algebra endomorphism. We then generalize the above classical notions fo
r Lie algebras to endo Lie algebras. As a result\, we obtain the notion of
coherent endomorphisms for each of the classes\, which then generalizes t
o the notion of coherent homomorphisms by a polarization process. The cohe
rent homomorphisms are compatible with the correspondences among the vario
us constructions\, as well as with the category of pre-Lie algebras. This
is a joint work with Chengming Bai and Yunhe Sheng.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Askar Dzhumadil'daev (Institute of Mathematics and Mathematical Mo
deling\, Kazakhstan)
DTSTART:20231218T070000Z
DTEND:20231218T080000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/10
DESCRIPTION:Title: Rota-Baxter algebras with non-zero weights\nby Askar Dzhuma
dil'daev (Institute of Mathematics and Mathematical Modeling\, Kazakhstan)
as part of Non-Associative Day in Online\n\n\nAbstract\nFor an associativ
e commutative algebra $A$ with Rota-Baxter operator $R : A \\to A$ with we
ight $\\lambda$ denote by $AR$ an algebra with linear space $A$ and multip
lication $a \\circ b = aR(b)$. Let $AR^{−}$ and $AR^{+}$ are algebra $AR
$ under Lie and Jordan commutators. If $\\lambda = 0$\, then the algebra $
AR = (A\, \\circ)$ is Zinbiel\, $AR^{+}$ is associative\, and $AR^{−}$ i
s Tortkara. We find polynomial identities of algebras $AR$\, $AR^{−}$ an
d $AR^{+}$ in case $\\lambda \\neq0$. We prove that $AR^{−}$ is Tortka
ra. $AR^{+}$ satisfies an identity of degree $5$. In case $\\lambda \\neq
0$\, the algebra $AR$ is not associative-admissible.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ievgen Makedonskyi (Beijing Institute of Mathematical Scienses and
applications\, China)
DTSTART:20231218T090000Z
DTEND:20231218T100000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/11
DESCRIPTION:Title: Duality Theorems for current Lie algebras\nby Ievgen Makedo
nskyi (Beijing Institute of Mathematical Scienses and applications\, China
) as part of Non-Associative Day in Online\n\n\nAbstract\nWe study some na
tural representations of current Lie algebras\, called Weyl modules. They
are natural analogues of irreducible representations of simple Lie algebra
s. There are several current analogues of classical theorems about Lie alg
ebras where these modules «play role» of irreducible modules. In my talk
\, I will explain analogues of duality theorems\, namely Peter-Weyl theore
m\, Schur-Weyl duality etc.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Kolesnikov (Sobolev Institute of Mathematics\, Russia)
DTSTART:20231218T110000Z
DTEND:20231218T120000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/12
DESCRIPTION:Title: Derived nonassociative algebras: identities and embedding probl
em\nby Pavel Kolesnikov (Sobolev Institute of Mathematics\, Russia) as
part of Non-Associative Day in Online\n\n\nAbstract\nGiven a nonassociati
ve algebra A with a derivation d\, let us define its derived algebra as th
e same linear space A equipped with two operations of multiplication \na$<
$b=ad(b)\, a$>$b=d(a)b\, for a\,b in A. The purpose of this talk is to sho
w how to derive the identities that hold on all such derived algebras prov
ided that A ranges through a given variety of nonassociative algebras. (In
particular\, for the variety of associative and commutative algebras the
result is very well known: the variety of Novikov algebras appears in thi
s way.) We also study the natural embedding problem related to the functor
transforming a differential algebra into its derived algebra. We state a
sufficient condition that guarantees an affirmative answer to the embeddin
g problem and show an example when the embedding problem has a negative so
lution.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Viruel (University of Malaga\, Spain)
DTSTART:20231218T120000Z
DTEND:20231218T130000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/13
DESCRIPTION:Title: Permutation represention of finite groups via automorphisms of
idempotent evolution algebras\nby Antonio Viruel (University of Malaga
\, Spain) as part of Non-Associative Day in Online\n\n\nAbstract\nIn the w
ake of the influential work by Elduque-Labra\, it is known that every fini
te dimensional evolution K-algebra X such that X^2=X\, namely X is idempot
ent\, has finite group of automorphisms. Building on this foundation\, wo
rks of Costoya et al. show that given any finite group G\, there exists an
idempotent finite-dimensional evolution algebra X such that Aut(X)\\cong
G. Moreover\, when the base field is sufficiently large in comparison to
the group G\, such an X can be selected to be simple. As a result\, Sriwo
ngsa-Zou propose that idempotent finite-dimensional evolution algebras can
be classified based on the isomorphism type of their group of automorphis
ms and dimension. Within this context\, we establish that the natural repr
esentation of highly transitive groups cannot be realized as the complete
group of automorphisms of an idempotent finite-dimensional evolution algeb
ra. For instance\, for any sufficiently large integer n\, there exists no
evolution algebra X such that X^2=X\, dim X=n\, and Aut(X) is isomorphic t
o the alternating group A_n. However\, we demonstrate that for any (not ne
cessarily faithful) permutation representation p : G -> S_n and any field
K\, there exists a finite-dimensional evolution K-algebra X such that X^2=
X\, Aut(X)\\cong G$ and the induced representation given by the Aut(X)-act
ion on the natural idempotents of X is p. This is a joint work with C. Cos
toya (U. Santiago Compostela) and Pedro Mayorga (U. Malaga).\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Olivier Mathieu (University of Lyon\, France)
DTSTART:20231218T130000Z
DTEND:20231218T140000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/14
DESCRIPTION:Title: On free Jordan Algebras\nby Olivier Mathieu (University of
Lyon\, France) as part of Non-Associative Day in Online\n\n\nAbstract\nThe
free Jordan algebra J(m) on m generators is an elusive object. It has bee
n determined when m=1 (folklore) and m=2 (Shirshov’s Theorem). Some part
ial informations are known in the case m=3\, namely the space of Jordan po
lynomial with three variables which are linear on the last one. We will pr
esent two conjectures. Conjecture 1\, which determines combinatorially the
structure of the homogenous components of J(m) is elementary but mysterio
us. Then we present Conjecture 2 about Lie algebra cohomology of a class o
f free Lie algebras in a certain category. Conjecture 2 is natural\, but n
ot elementary. Our main result is that Conjecture 2 implies Conjecture 1.
The proof\, which is quite long\, is based on the cyclicity of the Jordan
operad. Conjecture 1 has been checked up to degree 15 for m=2\, up to degr
ee 7 for m=3 and up to degree 6 for m>3. In the case m=1\, the conjecture
is equivalent to Jacobi triple identity. For conjecture 2\, the vanishing
of the cohomology has been proved up to degree 3 using polynomial functors
. In a recent work with J. Germoni\, we found two new special identities i
n degree 8 and 4 variables. These identities have been checked by computer
\, but the interesting point is that they were predicted by our conjecture
.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tom De Medts (Ghent University\, Belgium)
DTSTART:20231218T150000Z
DTEND:20231218T160000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/15
DESCRIPTION:Title: Primitive axial algebras of Jordan type and 3-transposition gro
ups\nby Tom De Medts (Ghent University\, Belgium) as part of Non-Assoc
iative Day in Online\n\n\nAbstract\nThe classification of 3-transposition
groups has a long history. In particular\, it is a highly non-trivial fact
that finitely generated 3-transposition groups are finite. We provide an
alternative viewpoint on this question using the corresponding “Matsuo a
lgebras”\, a class of non-associative algebras. These are instances of p
rimitive axial algebras of Jordan type. We prove that primitive 4-generate
d axial algebras of Jordan type are at most 81-dimensional (and this bound
is sharp). This is joint work with Louis Rowen and Yoav Segev (to appear
in Proc. AMS).\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sergey Shpectorov (University of Birmingham\, UK)
DTSTART:20231218T160000Z
DTEND:20231218T170000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/16
DESCRIPTION:Title: Solid subalgebras in algebras of Jordan type half\nby Serge
y Shpectorov (University of Birmingham\, UK) as part of Non-Associative Da
y in Online\n\n\nAbstract\nAlgebras of Jordan type $\\eta$ generalise in t
he axial context the class of Jordan algebras generated \nby primitive ide
mpotents. In addition to these examples\, arising for $\\eta=\\frac{1}{2}$
\, the class of \nalgebras of Jordan type includes the Matsuo algebras\, c
onstructed in terms of $3$-transposition groups \nfor all values of $\\eta
$. Classification of algebras of Jordan type for $\\eta\\neq\\frac{1}{2}$
was completed \nby Hall\, Rerhen and Shpectorov in 2015\, with a correctio
n by Hall\, Segev and Shpectorov in 2018. The \ncase of $\\eta=\\frac{1}{2
}$ remains open.\n\nAmong the known results about algebras of Jordan type
half are the classification\, in the above mentioned \npaper from 2015\, o
f $2$-generated algebras\, the classification of $3$-generated algebras by
Gorshkov \nand Staroletov in 2020\, and the recent (from 2023) result by
De Medts\, Rowen and Segev bounding the \ndimension of $4$-generated algeb
ras by $81$.\n\nIn the talk we will discuss another recent (in preparation
\, 2023) result on the subject\, by Gorshkov\, \nStaroletov and Shpectorov
. A $2$-generated subalgebra $B$ of an algebra $A$ of Jordan type half is
called \n\\emph{solid} if every primitive idempotent from $B$ is an axis i
n the entire $A$. Surprisingly\, it turned \nout that\, at least in charac
teristic zero\, almost all $2$-generated subalgebras are solid. More\, pre
cisely\, \na non-solid $2$-generated subalgebra is necessarily of type $3C
(\\frac{1}{2})$. Consequently\, if a \nfinite-dimensional algebras of Jord
an type half has a finite automorphism group then it is either a Matsuo \n
algebra or a factor of Matsuo algebra.\n\nThe above result hints of a poss
ibility of a geometric theory of algebras of Jordan type half.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jason Gaddis (Miami University\, USA)
DTSTART:20231218T170000Z
DTEND:20231218T180000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/17
DESCRIPTION:Title: Rigidity of quadratic Poisson algebras\nby Jason Gaddis (Mi
ami University\, USA) as part of Non-Associative Day in Online\n\n\nAbstra
ct\nThe Shephard-Todd-Chevalley Theorem gives conditions for the invariant
ring of a polynomial ring to again be polynomial. However\, this behavior
is rarely observed for noncommutative algebras. For example\, the invaria
nt ring of the first Weyl algebra by a finite group is not isomorphic to t
he first Weyl algebra. In this talk\, I will discuss this rigidity in the
context of quadratic Poisson algebras. A key example will be those Poisson
polynomial algebras with skew-symmetric structure. This is joint work wit
h Padmini Veerapen and Xingting Wang.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Vesselin Drensky (Institute of Mathematics and Informatics\, Bulga
rian Academy of Sciences\, Bulgaria)
DTSTART:20231218T080000Z
DTEND:20231218T090000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/18
DESCRIPTION:Title: The Specht problem for varieties of Z n -graded Lie algebras in
positive characteristic\nby Vesselin Drensky (Institute of Mathematic
s and Informatics\, Bulgarian Academy of Sciences\, Bulgaria) as part of N
on-Associative Day in Online\n\n\nAbstract\nLet K be a field of positive c
haracteristic p and let UT p+1 (K) be the algebra of (p+1)×(p+1) upper tr
iangular matrices. We construct three varieties of Z p+1 -graded Lie algeb
ras which do not have a finite basis of their graded identities and satisf
y the graded identities which in the case of infinite field define the var
iety generated by UT p+1 (K). The first variety contains the other two. Th
e second one is locally finite. The third variety is generated by a finite
dimensional algebra over an infinite field. These results are in the spir
it of similar results obtained in the 1970s and 1980s for non-graded Lie a
lgebras in positive characteristic.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Zhanqiang Bai (Soochow University\, China)
DTSTART:20241223T080000Z
DTEND:20241223T090000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/19
DESCRIPTION:Title: Gelfand-Kirillov dimensions of highest weight modules of simple
Lie algebras\nby Zhanqiang Bai (Soochow University\, China) as part o
f Non-Associative Day in Online\n\n\nAbstract\nGelfand-Kirillov dimension
is an important invariant\, which was introduced by Gelfand and Kirillov i
n 1960s. This invariant usually can measure the size of the infinite-dimen
sional algebraic structures. In this talk\, by using Lusztig's a-function
and based on our previous work\, we will give an algorithm to compute the
Gelfand-Kirillov dimensions of highest weight modules of exceptional type
Lie algebras.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cindy Tsang (Ochanomizu University in Tokyo\, Japan)
DTSTART:20241223T090000Z
DTEND:20241223T100000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/20
DESCRIPTION:Title: On Grün's lemma for perfect skew braces\nby Cindy Tsang (O
chanomizu University in Tokyo\, Japan) as part of Non-Associative Day in O
nline\n\n\nAbstract\nThe well-known Grün’s lemma in group theory states
that the quotient of a perfect group by its center is always centerless.
In this talk\, we shall consider its analog in the setting of skew brace\,
an algebraic structure that was introduced in the study of set-theoretic
solutions to the Yang-Baxter equation. Here we shall use the annihilator o
f a skew brace as an analog of the center of a group. Our main result is
that the analog of Grün’s lemma always holds for two-sided perfect skew
braces but fails in general.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucio Centrone (University of Bari\, Italy)
DTSTART:20241223T100000Z
DTEND:20241223T110000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/21
DESCRIPTION:Title: On geometries arising from varieties of algebras\nby Lucio
Centrone (University of Bari\, Italy) as part of Non-Associative Day in On
line\n\n\nAbstract\nWe will construct geometric objects via varieties of a
lgebras and we shall see how they interplay in the light of their polynomi
al identities.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kurusch Ebrahimi-Fard (Norwegian University of Science and Technol
ogy\, Norway)
DTSTART:20241223T120000Z
DTEND:20241223T130000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/22
DESCRIPTION:Title: A post-group theoretic perspective on the operator-valued S-tra
nsform in free probability\nby Kurusch Ebrahimi-Fard (Norwegian Univer
sity of Science and Technology\, Norway) as part of Non-Associative Day in
Online\n\n\nAbstract\nWe discuss the algebraic structure underlying Voicu
lescu's S-transform in operator-valued free probability. It is shown how i
ts twisted factorisation property gives rise to post-groups\, crossed morp
hisms\, as well as pre- and post-Lie algebras. Based on joint work with T.
Ringeard (arXiv:2402.16450).\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mahender Singh (IISER Mohali\, India)
DTSTART:20241223T130000Z
DTEND:20241223T140000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/23
DESCRIPTION:Title: Idempotents of quandle rings and application to knots\nby M
ahender Singh (IISER Mohali\, India) as part of Non-Associative Day in Onl
ine\n\n\nAbstract\nQuandles are non-associative algebraic structures arisi
ng from the algebraic formulation of the Reidemeister moves of planar diag
rams of knots. Quandle rings were introduced recently as analogues of grou
p rings for quandles. In this talk\, we will explore the idempotents of qu
andle rings and their connection to quandle coverings. We show that integr
al quandle rings of finite-type quandles\, which are non-trivial coverings
of well-behaved base quandles\, possess infinitely many non-trivial idemp
otents\, and offer a complete characterization of these idempotents. Addit
ionally\, we show that integral quandle rings of free quandles contain onl
y trivial idempotents\, thereby identifying an infinite family of quandles
with this property. In terms of applications to knot theory\, we present
explicit examples of knots where coloring with idempotents yields stronger
invariants compared to the traditional quandle coloring invariant.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Antonio Peralta (University of Granada\, Spain)
DTSTART:20241223T140000Z
DTEND:20241223T150000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/24
DESCRIPTION:Title: Maps preserving $\\lambda$-Aluthge transforms on product\nb
y Antonio Peralta (University of Granada\, Spain) as part of Non-Associati
ve Day in Online\n\n\nAbstract\nGiven $\\lambda \\in[0\,1]\,$ the \\emph{$
\\lambda$-Aluthge transform} of an element $a$ in a von Neumann algebra $M
$ is defined by $\\Delta_{\\lambda}(a)=|a|^{\\lambda} u |a|^{1-\\lambda}\,
$ where $a = u |a|$ is the polar decomposition of $a$ in $M$. This talk wi
ll be devoted to survey some of the main conclusions on bijective maps bet
ween von Neumann algebras commuting with the $\\lambda$-Aluthge transform
on products of the form $a b$\, $ab^*$\, $a\\circ b$ and $a\\circ b^*$\, w
here $\\circ$ denotes the natural Jordan product. We shall show that all t
hese maps are naturally linked to the Jordan structure of the von Neumann
algebras. We shall also see how these problems are naturally connected wit
h those classical studies by J. Hakeda and K. Saito on linear bijections b
etween von Neumann algebras preserving products of the form $a b$ and $a\\
circ b$.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Valeriy Bardakov (Sobolev Institute of Mathematics\, Russia)
DTSTART:20241223T160000Z
DTEND:20241223T170000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/25
DESCRIPTION:Title: Rota-Baxter operators on groups\, ranks\, and algebras\nby
Valeriy Bardakov (Sobolev Institute of Mathematics\, Russia) as part of No
n-Associative Day in Online\n\n\nAbstract\nRota--Baxter operators (RB-oper
ators) for commutative algebras were introduced by Baxter in 1960. Since t
hen\, the theory of Rota-Baxter operators has undergone extensive developm
ent by various authors in different fields of mathematics. In 2021 L. Guo\
, H. Lang\, and Y. Sheng defined a Rota--Baxter operator on groups and pro
ved that if $G$ is a Lie group and $B \\colon G \\to G$ is a Rota--Baxter
operator\, then the tangent map $B$ at identity is a Rota--Baxter operator
on the Lie algebra of $G$. In 2024 V.G. Bardakov and V.A. Bovdi introdu
ced Rota--Baxter operators on racks and quandles. In my talk\, I will giv
e a survey of results that we have found with my colleagues during the las
t few years and which are dedicated to RB--operators on groups\, racks\,
and Hopf algebras.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:James Zhang (University of Washington\, USA)
DTSTART:20241223T180000Z
DTEND:20241223T190000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/26
DESCRIPTION:Title: Poisson valuations and applications\nby James Zhang (Univer
sity of Washington\, USA) as part of Non-Associative Day in Online\n\n\nAb
stract\nWe introduce the notation of a Poisson valuation and use it to stu
dy automorphism\, isomorphism\, and embedding problems for several classes
of Poisson algebras/fields. This is joint work with Hongdi Huang\, Xin Ta
n\, and Xingting Wang\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Tatiana Gateva-Ivanova (American University in Bulgaria\, Bulgaria
)
DTSTART:20241223T170000Z
DTEND:20241223T180000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/27
DESCRIPTION:Title: Quadratic algebras and idempotent braided sets\nby Tatiana
Gateva-Ivanova (American University in Bulgaria\, Bulgaria) as part of Non
-Associative Day in Online\n\n\nAbstract\nWe study the Yang-Baxter algebra
s $A(K\,X\,r)$ associated to finite set-theoretic solutions $(X\,r)$ of th
e braid relations. We introduce an equivalent set of quadratic relations $
R \\subseteq G$\, where $G$ is the reduced Gr\\"{o}bner basis of $R$. We s
how that if $(X\,r)$ is left-nondegenerate and idempotent then $R=G$ and t
he Yang-Baxter algebra is PBW. We use graphical methods to study the globa
l dimension of n-generated PBW algebras in the general case and apply this
to Yang-Baxter algebras in the left-nondegenerate idempotent case. We stu
dy the d-Veronese subalgebras for a class of quadratic algebras and use th
is to show that for $(X\,r)$ left-nondegenerate idempotent\, the d-Verones
e subalgebra $A^{(d)}$ of $A =A(K\,X\,r)$ can be identified with $A(K\,X\,
r^{(d)})$\, where $(X\,r^{(d)})$ are left-nondegenerate idempotent solutio
ns for all $d \\geq 2$. We determined the Segre product in the left-nondeg
enerate idempotent setting. Our results apply to a previously studied clas
s of `permutation idempotent' solutions\, where we show that all their Yan
g-Baxter algebras for a given cardinality of $X$ are isomorphic and are is
omorphic to their d-Veronese subalgebras. In the linearised setting\, we c
onstruct the Koszul dual of the Yang-Baxter algebra and the Nichols-Worono
wicz algebra in the idempotent case\, showing that the latter is quadratic
. We also construct noncommutative differentials on some of these quadrati
c algebras. This talk is based on a joint work with Shahn Majid.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bauyrzhan Sartayev (Narxoz University\, Kazakhstan)
DTSTART:20251222T080000Z
DTEND:20251222T090000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/28
DESCRIPTION:Title: On the Malcev classification for the variety of associative alg
ebras\nby Bauyrzhan Sartayev (Narxoz University\, Kazakhstan) as part
of Non-Associative Day in Online\n\n\nAbstract\nIn this talk\, we consider
four types of subvarieties of the variety of associative algebras. We stu
dy these subvarieties from the point of view of operads and show their con
nections with well-known classes of algebras\, such as dendriform algebras
and noncommutative Novikov algebras. Also\, we define the commutator and
anti-commutator operations on these algebras and derive several identities
satisfied by these operations. For the second and third types of associat
ive algebras\, we construct the bases for the corresponding free algebras.
Finally\, we prove that a free metabelian Lie algebra can be embedded in
to a free associative algebra of the second type.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Solomon Vishkautsan (Tel-Hai Academic College\, Israel)
DTSTART:20251222T090000Z
DTEND:20251222T100000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/29
DESCRIPTION:Title: Eigenvalues and linear recurrence relations over the Octonions<
/a>\nby Solomon Vishkautsan (Tel-Hai Academic College\, Israel) as part of
Non-Associative Day in Online\n\n\nAbstract\nI will discuss joint work wi
th Adam Chapman and Ilan Levin\, regarding algorithms for: finding left/ri
ght eigenvalues of Octonion matrices (2x2 so far)\, and solving linear rec
urrences of order 2 over the Octonions.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Kolesnikov (Sobolev Institute of Mathematics\, Russia)
DTSTART:20251222T100000Z
DTEND:20251222T110000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/30
DESCRIPTION:Title: Dendriform splitting and chiral algebras\nby Pavel Kolesnik
ov (Sobolev Institute of Mathematics\, Russia) as part of Non-Associative
Day in Online\n\n\nAbstract\nVertex algebras usually considered as a tool
in mathematical physics (conformal field theory) or representation theory
(infinite-dimensional Lie algebras and sporadic finite simple groups) may
be thought of as of deeply generalized analogues of Poisson algebras. Name
ly\, following B. Bakalov and V.G. Kac (2002)\, a vertex algebra is a bree
d of pre-Lie differential algebra and Lie conformal algebra structures. In
this talk\, we will observe several approaches to vertex algebras includi
ng the one via chiral operads. Within the latter approach\, a vertex algeb
ra is a morphism from the operad Lie to the chiral operad P^{ch}(V) constr
ucted on a space V with a single linear operator. We apply this approach t
o get the class of dendriform split systems (preLie chiral\, or pre-vertex
algebras) and study the left adjoint functor to the forgetful functor fro
m the category of pre-vertex algebras to preLie conformal algebras.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Lucio Centrone (University of Bari\, Italy)
DTSTART:20251222T120000Z
DTEND:20251222T130000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/31
DESCRIPTION:Title: On algebras with regular gradings\nby Lucio Centrone (Unive
rsity of Bari\, Italy) as part of Non-Associative Day in Online\n\n\nAbstr
act\nWe will show the latest results on algebras endowed with a regular gr
ading.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cindy Tsang (Ochanomizu University in Tokyo\, Japan)
DTSTART:20251222T130000Z
DTEND:20251222T140000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/32
DESCRIPTION:Title: Hopf--Galois structures of cyclic type on parallel extensions o
f prime power degree\nby Cindy Tsang (Ochanomizu University in Tokyo\,
Japan) as part of Non-Associative Day in Online\n\n\nAbstract\nLet $L/K$
be a finite separable extension with Galois closure $\\widetilde{L}/K$. We
say that $L'/K$ is parallel to $L/K$ if $L'$ is an immediate field of $\\
widetilde{L}/K$ and $[\\widetilde{L}:K]=[L:K]$. Note that this notion is n
ot symmetric. We are interested in comparing the Hopf-Galois structures on
$L'/K$ with those on $L/K$. In this talk\, I will first explain how this
problem reduces to a completely group-theoretic problem that involves the
study of transitive subgroups of the holomorph. After that\, I will report
on some new results when the type of the Hopf-Galois structures is cyclic
and the degree of the extension is a prime power. This is joint work with
Andrew Darlington.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anastasia Doikou (Heriot-Watt University\, UK)
DTSTART:20251222T140000Z
DTEND:20251222T150000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/33
DESCRIPTION:Title: Combinatorial Drinfel'd twists & the Yang-Baxter equation\n
by Anastasia Doikou (Heriot-Watt University\, UK) as part of Non-Associati
ve Day in Online\n\n\nAbstract\nWe introduce the special set-theoretic Yan
g-Baxter algebra and show that it is a Hopf algebra subject to certain con
ditions. The associated universal R-matrix is also obtained via an admissi
ble Drinfel'd twist. The structure of braces emerges naturally in this con
text by requiring the special set-theoretic Yang-Baxter algebra to be a Ho
pf algebra and a quasi-triangular bialgebra after twisting. The fundamenta
l representation of the universal R-matrix yields the familiar involutive
set-theoretic (combinatorial) solution of the Yang-Baxter equation. We als
o introduce rack Hopf-like algebras and obtain rack and quandle solutions
of the YBE. We show that the same combinatorial twist cane be used to pro
duce non-involutive set-theoretic solutions.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Marzia Mazzotta (University of Salento\, Italy)
DTSTART:20251222T160000Z
DTEND:20251222T170000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/34
DESCRIPTION:Title: Associative Pentagon Algebras\nby Marzia Mazzotta (Universi
ty of Salento\, Italy) as part of Non-Associative Day in Online\n\n\nAbstr
act\nA set-theoretical solution of the Pentagon Equation can be described
in terms of a \\emph{pentagon algebra} $(S\, +\, \\ast)$\, namely\, a set
equipped with two binary operations where $(S\,+)$ forms a semigroup and
the operations $+$ and $\\ast$ satisfy additional compatibility conditions
arising from the Pentagon Equation. In this talk\, we introduce an algebr
aic framework for studying such structures and outline several strategies
for constructing and classifying their solutions. Our attention will be de
voted in particular to the case in which the second operation $\\ast$ is a
lso associative. We present characterizations of these algebras\, together
with structural consequences for the interaction between the two operatio
ns. Moreover\, we will present some recent results from an ongoing collabo
ration with Agata Pilitowska and Arne Van Antwerpen.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Maxime Fairon (Université Bourgogne Europe\, France)
DTSTART:20251222T170000Z
DTEND:20251222T180000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/35
DESCRIPTION:Title: Double Poisson algebra cohomology\nby Maxime Fairon (Univer
sité Bourgogne Europe\, France) as part of Non-Associative Day in Online\
n\n\nAbstract\nThe structure of a double Poisson algebra (as introduced by
Van den Bergh) induces a structure of Poisson algebra on each of its repr
esentation algebras. For these\, a cohomology theory (initiated by Pichere
au and Van de Weyer) can be constructed under mild conditions\, and it get
s mapped to the usual Poisson cohomology of the corresponding representati
on algebras. My aim is to recall this original construction\, and then I w
ill explain a far-reaching generalisation leading to several other cohomol
ogy theories of a similar nature. This talk is meant to be an overview of
Part 1 of arXiv:2509.21232 (joint with Daniele Valeri).\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Artem Lopatin (University of Campinas\, Brazil)
DTSTART:20251222T180000Z
DTEND:20251222T190000Z
DTSTAMP:20260422T225721Z
UID:NonAssociativeDay/36
DESCRIPTION:Title: Invariants for simple evolution algebras\nby Artem Lopatin
(University of Campinas\, Brazil) as part of Non-Associative Day in Online
\n\n\nAbstract\nGiven an algebra $\\mathcal{A}$\, the polynomial invariant
s $I_m(\\mathcal{A})$ of $m$-copies of $\\mathcal{A}$ with respect to the
action of the automorphism group of $\\mathcal{A}$ is a classical topic da
ting back to the 1970s\, beginning with works of Procesi and Sibirskii and
later extended by Iltyakov. Recently\, generators for $I_m(\\mathcal{A})$
were described for arbitrary two-dimensional algebras (Alvarez and Lopati
n\, 2025) and for arbitrary three-dimensional non-Lie Leibniz algebras (Ka
ygorodov and Lopatin) over the complex numbers. We continue this line of r
esearch by describing generators for $I_m(\\mathcal{A})$ when $\\mathcal{A
}$ is a three-dimensional simple evolution algebra.\n
LOCATION:https://researchseminars.org/talk/NonAssociativeDay/36/
END:VEVENT
END:VCALENDAR