Coquasitriangular Weak Hopf Group Algebras and Braided Monoidal Categories |
Received:June 05, 2013 Revised:September 02, 2014 |
Key Words:
$\pi$-$H$-comodules braided monoidal category coquasitriangular structure.
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Fund Project:Supported by the Natural Science Foundation of Jiangsu Province (Grant No.BK2012736) and the Fund of Science and Technology Department of Guizhou Province (Grant No.\,2014GZ81365). |
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Abstract: |
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 $\sigma$. |
Citation: |
DOI:10.3770/j.issn:2095-2651.2014.06.004 |
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