All Questions

It is well-known that the fusion category $\text{Rep}(D_4)$ of representations of the dihedral group $D_4$ of order 8 admits three distinct fiber functors. Therefore, there are three different Hopf ...

What is the smallest group $G$ such that $\operatorname{Rep}(G)$ has a non-symmetric braiding (or just an easy example)? I seem to remember a result classifying all universal $R$-matrices of $\mathbb ...

Let $k$ be a field, $G$ a finite group, and $k[G]$ the group algebra. Let $A$ be a subalgebra of $k[G]$. In general, $A$ is not the group algebra of some subgroup $H$ of $G$. Question: Is there any ...

Every group acts on itself by conjugation $h \mapsto g h g^{-1}$. Respectively considering functions on a group we obtain a linear representation. Question 1: what is known about this representation ...

I am interested in the following functor from Monoids (in $\text{Set}$) to Graded Lie Algebras (over a fixed field of characteristic $0$). (By "graded" I mean only that my Lie algebras have some ...

Related to a previous question I am asking furthermore a proof for the following: Question 1: If $\chi$ is a faithful irreducible character of a finite group $G$ then the regular character of $G$ is ...