Coquasitriangular Weak Hopf Group Algebras and Braided Monoidal Categories

DOI：10.3770/j.issn:2095-2651.2014.06.004

 作者 单位 郭双建 贵州财经大学数学与统计学院, 贵州 贵阳 550025

本文首先给出了交叉弱Hopf $\pi$-代数 $H$上的交叉左 $\pi$-$H$-余模, 并且证明了 交叉左 $\pi$-$H$-余模范畴是一个 monoidal 范畴. 最后, 证明了一簇$k$- 线性映射$\sigma=\{\sigma_{\a,\b}: H_{\a}\o H_{\b}\rightarrow k\}_{\a,\b\in \pi}$ 是交叉弱Hopf $\pi$-代数的余拟三角结构 的充要条件是 交叉左 $\pi$-$H$- 余模范畴是一个辫子monoidal 范畴.其中辫子是由 $\sigma$ 定义的.

In this paper, we first give the definitions of a crossed left $\pi$-$H$-comodules over a crossed weak Hopf $\pi$-algebra $H$, and show that the category of crossed left $\pi$-$H$-comodules is a monoidal category. Finally, we show that a family $\sigma=\{\sigma_{\a,\b}: H_{\a}\o H_{\b}\rightarrow k\}_{\a,\b\in \pi}$ of $k$-linear maps is a coquasitriangular structure of a crossed weak Hopf $\pi$-algebra $H$ if and only if the category of crossed left $\pi$-$H$-comodules over $H$ is a braided monoidal category with braiding defined by $\sigma$.