Quivers, Quasi-Quantum Groups and Finite Tensor Categories

Details Quivers, Quasi-Quantum Groups and Finite Tensor Categories Quivers, Quasi-Quantum Groups and Finite Tensor Categories

2009-06-18

arxiv.org/abs/0906.3415v1

Mathematics

Quantum Algebra

22 pages

Scientific paper

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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