Ann Kiefer
The VUB algebra seminar takes place on Tuedays 16h15-17h15 in room 6G324.

Due to the ongoing Coronavirus crisis, all seminars have been cancelled until April 20th (This period will probably be extended.)


Feb 2 Ofir Schnabel, Classifying crossed products up to several graded equivalence relations

A graded algebra is a crossed product if every homogeneous component admits an invertible element. Hence, natural examples of crossed products are group algebras, twisted group algebras, skew group algebras and graded division algebras. We will define some natural equivalence relations on graded algebras and we will illustrate how to classify crossed products up to these equivalence relations in terms of orbits with respect to certain group actions on crossed products. No prior knowledge is required. This is joint work with Yuval Ginosar.

Feb 11 Ilaria Colazzo, The algebraic structure of brace-like semi-trusses

To study set-theoretic solutions of the Yang-Baxter equation, several authors introduced algebraic structures. Rump, and Cedó, Jespers and Okniński introduced braces, Guarnieri and Vendramin introduced skew braces and Catino, Colazzo and Stefanelli, and Jespers and Van Antwerpen introduced semi-braces. All these objects are subclasses of (semi-)trusses, an algebraic structure introduced by Brzeziński to study the distributive law of (semi-)braces. In this talk, we focus on a subclass of left semi-trusses, the class of brace-like semi-trusses. First, we prove that in the finite case, the additive structure is a completely regular semigroup. Secondly, we apply this result on a specific instance of a left semi-truss called an almost left semi-brace, introduced by Miccoli to study its algebraic structure. In particular, we show that one can associate a left semi-brace to any almost left semi-brace. Furthermore, we show that the set-theoretic solutions of the Yang-Baxter equation originating from almost left semi-braces arise from this correspondence. This talk is based on joint work with Arne Van Antwerpen (arXiv:1908.11744)

Feb 18 Charlotte Verwimp, Structure monoids of set-theoretic solutions of the Yang-Baxter equation

Given a set-theoretic solution (X, r) of the Yang-Baxter equation, Gateva-Ivanova and Majid [2] showed that this solution can be extended to a solution (M(X, r), rM) on the so called structure monoid M(X, r), such that rM restricts to r on XxX. At the group level, this is no longer true. This shows the importance of looking at the structure monoid instead of the structure group. For (finite, bijective) left non-degenerate solutions, there is an important link between the structure monoid and another “richer” associative structure, called the derived structure monoid. Using this richer structure, one has been able to study algebraic properties of the structure monoid. In this talk, we take a better look at how Gateva-Ivanova and Majid extend an arbitrary set-theoretic solution of the Yang-Baxter equation to a solution on the structure monoid. Next, we generalize the link between the structure monoid and the derived structure monoids for arbitrary set-theoretic solutions of the Yang-Baxter equation. The latter is based on some new results of a joint work with Ferran Cedó and Eric Jespers [1]. Finally, we pose questions and discuss recent results on non-degenerate and bijective solutions.

[1] F. Cedó, E. Jespers, C. Verwimp, Structure monoids of set- theoretic solutions of the Yang-Baxter equation, arXiv:1912.09710 [math.RA].

[2] T. Gateva-Ivanova and S. Majid, Matched pairs approach to set- theoretic solutions of the Yang-Baxter equation, J. Algebra 319 (2008), no. 4, 1462–1529.

Feb 25 Réamonn Ó Buachalla,

Mar 3 Abel Lacabanne, An asymptotic cellular category for G(e,e,n)

Given a Coxeter system (W,S), one can associate a Hecke algebra which is a deformation of the group algebra of W. Kazhdan and Lusztig have constructed another basis of this algebra, which is then used to develop a cell theory for Coxeter groups. Bonnafé and Rouquier developed a theory of cells for complex reflection groups which is conjectured to be a generalization of the Kazhdan-Lusztig theory.
In this talk, I will first review the case of finite Coxeter groups and (briefly) the categorification of Hecke algebras using Soergel bimodules. Then I will focus on the complex reflection group G(e,e,n) and one particular two-sided cell. A category arising from the quantum enveloping algebra of sln will be constructed and I hope to explain why it can be considered as an asymptotic cell category for the complex reflection group G(e,e,n).

Mar 10 Leandro Vendramin, On the classification of Nichols algebras

Nichols algebras appear in several branches of mathematics going from Hopf algebras and quantum groups, to Schubert calculus and conformal field theories. In this talk, we review the main problems related to Nichols algebras and we discuss some classification theorems. The talk is mainly based on joints works with I. Heckenberger.

Mima Stanojkovski, Automorphism groups, elliptic curves, and the PORC conjecture

In 1960, Graham Higman formulated his famous PORC conjecture in relation to the function f(p,n) counting the isomorphism classes of p-groups of order p^n . By means of explicit formulas, the PORC conjecture has been verified for n < 8. Despite that, it is still open and has in recent years been questioned. I will discuss (generalizations of) an example of du Sautoy and Vaughan-Lee (2012), together with a conceptualization of the phenomena they observe. Hidden heroes of this story turn out to be Hessian matrices and torsion points of elliptic curves. This is joint work with Christopher Voll.

Mar 17 Seminar Cancelled,

Mar 24 Seminar Cancelled,

Mar 31 Seminar Cancelled,

Avr 7 Seminar Cancelled,

Avr 14 Seminar Cancelled,

Avr 21 Theo Raedschelders,

Avr 24 Marco Bonatto,

Avr 28 free slot,

May 5 Eugenio Gianelli + Carolina Vallejo,

May 12 free slot,

May 19 free slot,

May 26 Martina Lanini,

Jun 2 Mandi Schaeffer-Fry,

Jun 3 Tomasz Brzezinski,

Jun 9 free slot,

Jun 16 free slot,

Jun 23 free slot,

Jun 30 free slot,