Fusion Systems of Blocks of Finite Groups over Arbitrary Fields

Abstract: Given a field $k$ of characteristic $p > 0$, a finite group $G$, to any block idempotent $b$ of the group algebra $kG$, Puig associated a fusion system and proved that it is saturated if the $k$-algebra $kC_G(P)e$ is split, where $(P,e)$ is a maximal $b$-Brauer pair. In this talk, we will investigate in the non-split case how far the fusion system is from being saturated by describing it in an explicit way as being generated by the fusion system of a related block idempotent over a larger field together with a single automorphism of the defect group.

combinatoricscomplex variablesfunctional analysisgeneral mathematicsgroup theoryK-theory and homologynumber theoryoperator algebrasprobabilityquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the discipline

GAG seminar

Series comments: Description: Non-specialized research seminar