turkmath.org

Let $G$ be a finite group and $k$ be a field of characteristic $p>0$. Puig associated a fusion system to a block idempotent of $kG$ and proved that this block fusion system is saturated if $k$-algebra $kC_G(P)e$ is split, where $(P,e)$ denotes 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. This is a joint work with Robert Boltje (UC Santa Cruz) and Deniz Yılmaz (Bilkent University).