Article ID Journal Published Year Pages File Type
4588209 Journal of Algebra 2007 10 Pages PDF
Abstract

A recent result by H. Meyer shows that, for a field F of characteristic p>0 and a finite group G with an abelian Sylow p-subgroup, the F-subspace Zp′FG of the group algebra FG spanned by all p-regular class sums in G is multiplicatively closed, i.e. a subalgebra of the center ZFG of FG. Here we generalize this result to blocks. More precisely, we show that, for a block A of a group algebra FG with an abelian defect group, the F-subspace Zp′A:=A∩Zp′FG is multiplicatively closed, i.e. a subalgebra of the center ZA of A. We also show that this subalgebra is invariant under perfect isometries and hence under derived equivalences.

Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory