Yetter-Drinfeld categories for quasi-Hopf algebras

Bulacu, D.; Caenepeel, S.; Panaite, F.

Yetter-Drinfeld categories for quasi-Hopf algebras

Authors

Bulacu, D.

Caenepeel, S.

Panaite, F.

Description

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