On the tensor product of bimodule categories over Hopf algebras

TL;DR

This paper describes the tensor product of bimodule categories over the representation category of a finite-dimensional Hopf algebra, providing explicit descriptions for invertible cases and exploring consequences for pointed Hopf algebras.

Contribution

It offers a new explicit description of the tensor product of bimodule categories over Rep(H), especially for invertible bimodule categories, with applications to pointed Hopf algebras.

Findings

Explicit description of tensor products over Rep(H)

Characterization of invertible bimodule categories

Applications to pointed Hopf algebras

Abstract

Let H be a finite-dimensional Hopf algebra. We give a description of the tensor product of bimodule categories over Rep(H). When the bimodule categories are invertible this description can be given explicitly. We present some consequences of this description in the case H is a pointed Hopf algebra.