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

Abstract

Given a Hopf algebra $H$ and a projection $H\to A$ to a Hopf subalgebra, we construct a Hopf algebra $r(H)$, 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, arxiv:1111.4673 . We prove a braided equivalence between the Yetter-Drinfel'd modules over a Hopf algebra and its partial dualization.