Quasi-elementary H-Azumaya Algebras Arising from Generalized (Anti) Yetter-Drinfeld Modules

Abstract

Let H be a Hopf algebra with bijective antipode, α, β ∈ Aut Hopf (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.