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.