A note on blocks with abelian defect groups

作者：Fan Yun; Kuelshammer Burkhard

来源：Journal of Algebra, 2007, 317(1): 250-259.

DOI：10.1016/j.jalgebra.2007.03.043

• representation theory of finite groups
• block theory

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 Z(p') 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 Z(p') A := A boolean AND Z(p') 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.

• 出版日期2007-11-1
• 单位华中师范大学