Abstract
Let π be a group, and H be a semi-Hopf π-algebra. We first show that the category H M of left π-modules over H is a monoidal category with a suitably defined tensor product and each element α in π induces a strict monoidal functor \({F_\alpha }\) from H M to itself. Then we introduce the concept of quasitriangular semi-Hopf π-algebra, and show that a semi-Hopf π-algebra H is quasitriangular if and only if the category H Mis a braided monoidal category and \({F_\alpha }\) is a strict braided monoidal functor for any α ∈ π. Finally, we give two examples of Hopf π-algebras and describe the categories of modules over them.
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This work is supported by NSF of China, No. 11171291, by Doctorate United Foundation, No. 20123250110005, of Ministry of China and Jiangsu Province, and by Qing Lan Project of Jiangsu Province.
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Zhao, S., Wang, J. & Chen, HX. Quasitriangular Hopf group algebras and braided monoidal categories. Czech Math J 64, 893–909 (2014). https://doi.org/10.1007/s10587-014-0142-5
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DOI: https://doi.org/10.1007/s10587-014-0142-5