Yetter-Drinfeld Modules for Weak Hom-Hopf Algebras

Abstract

The aim of this paper is to define and study Yetter-Drinfeld modules over weak Hom-Hopf algebras.
We show that the category ${}_H{\cal
WYD}^H$ of Yetter-Drinfeld modules with bijective structure maps over weak Hom-Hopf algebras is a rigid category and a braided monoidal category, and obtain a new solution of quantum Hom-Yang-Baxter equation. It turns out that, If $H$ is quasitriangular (respectively,
coquasitriangular)weak Hom-Hopf algebras, the category of modules (respectively, comodules) with bijective structure maps over $H$ is a braided monoidal subcategory of the category ${}_H{\cal
WYD}^H$ of Yetter-Drinfeld modules over weak Hom-Hopf algebras.