The Equivariant Brauer Group of a Cocommutative Hopf Algebra

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)-> BRM(k, H)->((pi) over tilde)Gal(k, H) is obtained. Furthermore, we prove the surjectivity of (pi) over tilde under certain circumstances. This generalizes Beattie's exact sequence to the "infinite" case.