Yetter-Drinfeld Categories for Quasi-Hopf Algebras

Abstract

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 of finite dimensional left Yetter-Drinfeld modules is rigid, and then we compute explicitly the canonical isomorphisms in . Finally, we show that certain duals of H 0, the braided Hopf algebra (introduced in Bulacu and Nauwelaerts, 2002; Bulacu et al., 2000) are isomorphic as braided Hopf algebras if H is a finite dimensional triangular quasi-Hopf algebra. Communicated by M. Takeuchi.