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arXiv · 1611.04096

Finite quasi-quantum groups of diagonal type

Hua-Lin Huang·Gongxiang Liu·Yuping Yang·Yu Ye
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Abstract

The goal of the present paper is to classify an interesting class of elementary quasi-Hopf algebras, or equivalently, finite-dimensional pointed Majid algebras. By a Tannaka-Krein type duality, this determines a big class of pointed finite tensor categories. Based on some interesting observations of normalized 3-cocycles on finite abelian groups, we elucidate an explicit connection between our objective pointed Majid algebras and finite-dimensional pointed Hopf algebras over finite abelian groups. With a help of this connection and the successful theory of diagonal Nichols algebras over abelian groups, we provide a conceptual classification of finite-dimensional graded pointed Majid algebras of diagonal type. Some efficient methods of construction are also given.

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BibTeXRIS

Hua-Lin Huang, Gongxiang Liu, Yuping Yang, Yu Ye. 2016-12-20. Finite quasi-quantum groups of diagonal type. https://doi.org/10.1515/2017-0058

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