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From projective representations to quasi-quantum groups

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Abstract

This is a contribution to the project of quiver approaches to quasi-quantum groups. We classify Majid bimodules over groups with 3-cocycles by virtue of projective representations. This leads to a theoretic classification of graded pointed Majid algebras over path coalgebras, or equivalently cofree pointed coalgebras, and helps to provide a projective representation-theoretic description of the gauge equivalence of graded pointed Majid algebras. We apply this machinery to construct some concrete examples and obtain a classification of finite-dimensional graded pointed Majid algebras with the set of group-likes equal to the cyclic group of order 2.

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Correspondence to HuaLin Huang.

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Huang, H. From projective representations to quasi-quantum groups. Sci. China Math. 55, 2067–2080 (2012). https://doi.org/10.1007/s11425-012-4437-4

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