More properties of Yetter-Drinfeld category over dual quasi-Hopf algebras

Published 4 Dec 2015 in math.RA | (1512.01357v3)

Abstract: Let $H$ be a dual quasi-Hopf algebra. In this paper we will firstly introduce all possible categories of Yetter-Drinfeld modules over $H$, and give explicitly the monoidal and braided structure of them. Then we prove that the category $^{H_H\mathcal{YD}^{fd}$} of finite-dimensional left-left Yetter-Drinfeld modules is rigid. Finally we will study the braided cocommunitivity of $H_0$ in $^{H_H\mathcal{YD}$.}