Partially dualized Hopf algebras have equivalent Yetter–Drinfel'd modules

Given a Hopf algebra H   and a projection H→AH→A to a Hopf subalgebra, we construct a Hopf algebra r(H)r(H), called the partial dualization of H, with a projection to the Hopf algebra dual to A. This construction provides powerful techniques in the general setting of braided monoidal categories. The construction comprises in particular the reflections of generalized quantum groups [9]. We prove a braided equivalence between the Yetter–Drinfel'd modules over a Hopf algebra and its partial dualization.