Geodesic
Quasitriangular Hopf group algebras and braided monoidal categories
Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 893-909
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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.
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.
DOI : 10.1007/s10587-014-0142-5
Classification : 08C05, 16T05, 16T25, 18D10
Keywords: Hopf $\pi $-algebra; $H$-$\pi $-modules; braided monoidal category; braided monoidal functor 
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     title = {Quasitriangular {Hopf} group algebras and braided monoidal categories},
     journal = {Czechoslovak Mathematical Journal},
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     year = {2014},
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Zhao, Shiyin; Wang, Jing; Chen, Hui-Xiang. Quasitriangular Hopf group algebras and braided monoidal categories. Czechoslovak Mathematical Journal, Tome 64 (2014) no. 4, pp. 893-909. doi: 10.1007/s10587-014-0142-5

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