Abstract
For a commutative ring R and a Hopf algebra H which is finitely generated projective as an R-module, it is established that there is an (anti)-isomorphism of groups between the Brauer group BQ(R, H) of Hopf Yetter-Drinfel’d H-module algebras and the Brauer group of Hopf Yetter-Drinfel’d -module algebras, where is the linear dual of H. In this paper, we generalize this result by establishing an anti-isomorphism of groups between BQ(S, H), the Brauer group of dyslectic Hopf Yetter-Drinfel’d (S, H)-module algebras and , the Brauer group of dyslectic Hopf Yetter-Drinfel’d -module algebras, where S is an H-commutative Hopf Yetter-Drinfel’d H-module algebra and Sop is the opposite algebra of S.
Communicated by Alberto Elduque
2020 MATHEMATICS SUBJECT CLASSIFICATION: