Computing the Brauer-Long group of a Hopf algebra II: the Skolem-Noether theory

Abstract

Let H be a commutative, cocommutative and faithfully projective Hopf algebra over a commutative ring R. Then Long's Brauer group of H-dimodule algebras fits into an exact sequence 1→BD s(R,H)→BD(R,H) → β O(R,H) min, where O(R,H) min is a well-defined subgroup of the group of Hopf algebra automorphisms of H⊗ H ∗. It is not known whether β is surjective, but some partial results are given. The theory is applied to Orzech's and Deegan's subgroups of the Brauer-Long group.