London Algebra Colloquium abstract

Crossed products, Brauer groups and Clifford algebras

Andrei Marcus (Babes–Bolyai University), 29th April 2010

Abstract

We introduce an equivalence between central simple strongly G-graded algebras. Such classes are associated in a natural way to absolutely irreducible characters of semisimple G-graded algebras. We study invariants of this equivalence relation, and also the structure of certain representatives of the equivalence classes. We show that G-graded Rickard equivalences defined over small fields preserve Clifford classes associated to characters. These equivalences are compatible with operation on Clifford classes defined in terms of central simple crossed products.