Quasitriangular Hopf group algebras and braided monoidal categories

Czechoslovak Mathematical Journal

Shiyin Zhao¹  Jing Wang² 

[1] Department of Teachers Education, Suqian College, 399 South Huanghe Rd., Suqian, Jiangsu, 223800, P. R. China;Hui-Xiang Chen (corresponding author), School of Mathematical Science, Yangzhou University, 180 Siwangting Rd., Yangzhou, Jiangsu, 225002, P. R. China

关键词: Hopf $\pi$-algebra;    $H$-$\pi$-modules;    braided monoidal category;    braided monoidal functor;   

DOI  :  

学科分类：数学（综合）

来源: Akademie Ved Ceske Republiky

【 摘 要 】

Let $\pi$ be a group, and $H$ be a semi-Hopf $\pi$-algebra. We first show that the category $_H{\mathcal M}$ of left $\pi$-modules over $H$ is a monoidal category with a suitably defined tensor product and each element $\alpha$ in $\pi$ induces a strict monoidal functor $F_{\alpha}$ from $_H{\mathcal M}$ to itself. Then we introduce the concept of quasitriangular semi-Hopf $\pi$-algebra, and show that a semi-Hopf $\pi$-algebra $H$ is quasitriangular if and only if the category $_H\mathcal M$ is a braided monoidal category and $F_{\alpha}$ is a strict braided monoidal functor for any $\alpha\in\pi$. Finally, we give two examples of Hopf $\pi$-algebras and describe the categories of modules over them.

【 授权许可】

Unknown