1602.08731Feb 28, 2016

Yetter-Drinfeld modules for weak Hom-Hopf algebras

Shuangjian Guo, Yizheng Li, Shengxiang Wang

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 $H$

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is a braided monoidal subcategory of the category

{}_H{\cal WYD}^H

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

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