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arXiv · 0906.3415

Quivers, Quasi-Quantum Groups and Finite Tensor Categories

Hua-Lin Huang·Gongxiang Liu·Yu Ye
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Abstract

We study finite quasi-quantum groups in their quiver setting developed recently by the first author in arXiv:0902.1620 and arXiv:0903.1472. We obtain a classification of finite-dimensional pointed Majid algebras of finite corepresentation type, or equivalently a classification of elementary quasi-Hopf algebras of finite representation type, over the field of complex numbers. By the Tannaka-Krein duality principle, this provides a classification of the finite tensor categories in which every simple object has Frobenius-Perron dimension 1 and there are finitely many indecomposable objects up to isomorphism. Some interesting information of these finite tensor categories is given by making use of the quiver representation theory.

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BibTeXRIS

Hua-Lin Huang, Gongxiang Liu, Yu Ye. 2009-06-18. Quivers, Quasi-Quantum Groups and Finite Tensor Categories. https://doi.org/10.1007/s00220-011-1229-6

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