Characterization of quasi-Yetter–Drinfeld modules

Abstract

In this paper, we characterize quasi-Yetter–Drinfeld modules over a Hopf algebra [Formula: see text], which was introduced in [Y. Bazlov and A. Berenstein, Braided doubles and rational Cherednik algebras, Adv. Math. 220 (2009), 1466–1530]. We first show that the quasi-Drinfeld center of the category of [Formula: see text]-modules is equivalent to the category [Formula: see text] of quasi-Yetter–Drinfeld modules. Next, we prove that [Formula: see text] is equivalent to the category of generalized Hopf bimodules. Finally, we show that [Formula: see text] is also equivalent to the category of quasi-coactions over some Majid’s braided group if [Formula: see text] is quasi-triangular.