From projective representations to quasi-quantum groups

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• 作者：HuaLin Huang (1) hualin@sdu.edu.cn
• 关键词：Majid algebra – ; projective representation – ; Hopf quiver
• 刊名：SCIENCE CHINA Mathematics
• 出版年：2012
• 出版时间：October 2012
• 年：2012
• 卷：55
• 期：10
• 页码：2067-2080
• 全文大小：268.1 KB
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• 作者单位：1. School of Mathematics, Shandong University, Jinan, 250100 China
• ISSN：1869-1862

文摘

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.