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arXiv · 1602.08731

Yetter-Drinfeld modules for weak Hom-Hopf algebras

Shuangjian Guo·Yizheng Li·Shengxiang Wang
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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.

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Shuangjian Guo, Yizheng Li, Shengxiang Wang. 2016-02-28. Yetter-Drinfeld modules for weak Hom-Hopf algebras. https://arxiv.org/abs/1602.08731

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