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Quasitriangular Hopf Group Coalgebras and Braided Monoidal Categories

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Abstract

Turaev introduced the notions of group coalgebras, Hopf group coalgebras and quasitriangular Hopf group coalgebras. Virelizier studied algebraic properties of Hopf π-coalgebras. In this paper, we give the definitions of a (crossed) left H-π-modules over a (crossed) Hopf π-coalgebra H, and show that the categories of (crossed) left H-π-modules are both monoidal categories. Finally, we show that a family \({R=\{R_{\alpha, \beta} \in H_{\alpha} \otimes H_\beta\}_{\alpha, \beta\in\pi}}\) of elements is a quasitriangular structure of a crossed Hopf π-coalgebra H if and only if the category of crossed left H-π-modules over H is a braided monoidal category with braiding defined by R.

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Authors and Affiliations

  1. School of Mathematical Science, Yangzhou University, Yangzhou, 225002, China

    Meiling Zhu, Huixiang Chen & Libin Li

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  1. Meiling Zhu
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  2. Huixiang Chen
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  3. Libin Li
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Correspondence to Meiling Zhu.

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Zhu, M., Chen, H. & Li, L. Quasitriangular Hopf Group Coalgebras and Braided Monoidal Categories. Arab J Sci Eng 36, 1063–1070 (2011). https://doi.org/10.1007/s13369-011-0086-0

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  • DOI: https://doi.org/10.1007/s13369-011-0086-0

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