Yetter-Drinfeld categories for quasi-Hopf algebras

Abstract

We show that all possible categories of Yetter-Drinfeld modules over a quasi-Hopf algebra $H$ are isomorphic. We prove also that the category ^fd of finite dimensional left Yetter-Drinfeld modules is rigid and then we compute explicitly the canonical isomorphisms in ^fd. Finally, we show that certain duals of $H_0$, the braided Hopf algebra introduced in bn,bpv, are isomorphic as braided Hopf algebras if $H$ is a finite dimensional triangular quasi-Hopf algebra.