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

TL;DR

This paper constructs a class of H-Azumaya algebras from generalized Yetter-Drinfeld modules over a Hopf algebra with bijective antipode, linking them to the Brauer group.

Contribution

It introduces a new construction of H-Azumaya algebras from ( ext{α, β})-Yetter-Drinfeld modules and shows their subgroup structure within the Brauer group.

Findings

End(M) forms an H-Azumaya algebra under certain structures

The set of these H-Azumaya algebras forms a subgroup of BQ(k, H)

Provides a new perspective on the structure of H-Azumaya algebras

Abstract

Let H be a Hopf algebra with bijective antipode, let \alpha, \beta be two Hopf algebra automorphisms of H and M a finite dimensional (\alpha, \beta )-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.