Endomorphism algebras over weak (α, β)-Yetter–Drinfeld modules

Abstract

Let H be a weak Hopf algebra with a bijective antipode, α, β ∈ Aut weak Hopf (H) and M a finite-dimensional weak (α, β)-Yetter–Drinfeld module. Then in this paper we prove that the endomorphism algebras End Hs(M) and End Ht(M) op endowed with certain structures become algebras in H𝒲𝒴𝒟H and we also study the isomorphic relations between different endomorphism algebras. We prove that End Hs(M) endowed with certain structures becomes an H-Azumaya algebra.