Quasi-elementary H-Azumaya algebras arising from generalized (anti) Yetter-Drinfeld modules

Abstract

Let H be a Hopf algebra with bijective antipode, let α, βbe two Hopf algebra automorphisms of H and M a finite dimensional (α, β)-Yetter-Drinfeld module. We prove that End(M) endowed with certain structures becomes an H-Azumaya algebra, and the set of H-Azumaya algebras of this type is a subgroup of BQ(k, H), the Brauer group of H.

15 pages