The equivariant Brauer group of a cocommutative Hopf algebra

Abstract

We investigate the Brauer group BRM k H of a cocommutative Hopf algebra H (H can be nonfinitely generated). BRM k H is the bigger Brauer group of H-module Taylor–Azumaya algebras (which do not necessarily contain a unit). An exact sequence 1-->Br(k)-->BM(k,H)--> Gal(k,H) is obtained. Furthermore, we prove the surjectivity of ˜ under certain circumstances. This generalizes Beattie’s exact sequence to the “infinite” case.