Skew braces and the YBE
February 25
Quantum Yang–Baxter equation, Yetter–Drinfeld braces, and semi-abelian categories
In this talk, we show how to construct solutions of the quantum Yang–Baxter equation from Yetter–Drinfeld braces, algebraic structures that generalize cocommutative Hopf braces and are equivalent to matched pairs of actions on Hopf algebras. We further prove that cocommutative Yetter–Drinfeld braces (equivalently, cocommutative Hopf braces) form a semi-abelian category that is also strongly protomodular, as is the case for the categories of groups, skew braces, and cocommutative Hopf algebras. Moreover, under suitable assumptions on the base field, we show that skew braces and post-Lie algebras can be used to construct a torsion theory for this category. This talk is partially based on a joint work with D. Ferri and on a joint work with M. Gran.
February 11
On the total degree of a finite group
For a finite group $G$, the total degree $T(G)$ is defined as the sum of the degrees of the complex irreducible characters of $G$. We classify the groups with $T(G) \leq 100$, using computational methods, and investigate special cases such as groups of prime power order and groups with total degree the square of a prime. (This is joint work with László Héthelyi, Burkhard Külshammer, and Magdolna Szöke.)