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 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 WYD H of Yetter-Drinfeld modules over weak Hom-Hopf algebras.