On automorphisms and focal subgroups of blocks

2016/12/22 by Linckelmann, Markus
#FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1612.07739

Abstract

Given a p-block B of a finite group with defect group P and fusion system F on P we show that the rank of the group P/foc(F) is invariant under stable equivalences of Morita type. The main ingredients are the star-construction, due to Broue and Puig, a theorem of Weiss on linear source modules, arguments of Hertweck and Kimmerle applying Weiss' theorem to blocks, and connections with integrable derivations in the Hochschild cohomology of block algebras.

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