  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.

Quantum Algebra;Representation Theory