"Fusion Systems of Blocks: Part I"
Abstract: We understand a block of a ring to be a primitive idempotent of the centre of the ring. We shall be considering blocks of FG, where F is a large field of prime characteristic p and G is a finite group. In the 1940s, Brauer introduced the notion of a defect group D of a block b of FG. Such D is a p-subgroup of G, well-defined up to conjugacy. He also considered pairs (P, e) where P is a p-subgroup and e is a block of C(P) with defect group Z(P). In 1979, Alperin and Broue defined a Brauer pair to be a pair (P, e), as above, but without the condition on the defect group of e. In modern terminology, the pairs originally considered by Brauer are the centric Brauer pairs. The fusion system of b is a category whose objects are the Brauer pairs containing (1, b). Usually, we pass to an equivalent subcategory whose objects can be identified with the subgroups of a defect group D. Puig observed that the centric condition on a Brauer pair can be described entirely in terms of the fusion system.
Date: Tuesday, October 20, 2015
Place: Mathematics Seminar Room, SA-141
All are most cordially invited.
Tea and biscuits: before the seminar