# Darstellungstheorietage and Nikolaus Conference 2021

Speaker: Sofia Brenner (Jena)

Title: Socles of Centers of Group Algebras

Abstract:

For a finite-dimensional algebra $$A$$ over an algebraically closed field $$F$$, we consider the socle soc$$(Z(A))$$ of its center $$Z(A)$$. This space is known to be an ideal of $$Z(A)$$. In this talk, we are mainly concerned with the question under which conditions soc$$(Z(A))$$ is even an ideal of the algebra $$A$$ itself. We focus on the case that $$A = FG$$ is the group algebra of a finite group $$G$$ over $$F$$. In my talk, I will describe the structure of finite groups $$G$$ with the property that soc$$(ZFG)$$ is an ideal in $$FG$$ and state some partial classification results.