Yetter-Drinfeld-Long bimodules are modules

Abstract

Let $H$ be a finite dimensional bialgebra. In this paper, we prove that the category of Yetter-Drinfeld-Long bimodules is isomorphic to the Yetter-Drinfeld category over the tensor product bialgebra $HøH^{\ast }$ as monoidal category. Moreover if $H$ is a Hopf algebra with bijective antipode, the isomorphism is braided.

to appear in Czechoslovak Mathematical Journal