Reflection fusion categories

2018/03/15 by Pavel Etingof, César Galindo, Etingof, Pavel +1 · 1 citation
Mathematics · #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA

paper · pdf · doi:10.48550/arxiv.1803.05568

27 pages: references to MR2674592 and arXiv:0005291 are added

arxiv created 2018/04/16 · arxiv updated 2018/04/18

Abstract

We introduce the notion of a reflection fusion category, which is a type of a G-crossed category generated by objects of Frobenius-Perron dimension 1 and √(p), where p is an odd prime. We show that such categories correspond to orthogonal reflection groups over \mathbbF_p. This allows us to use the known classification of irreducible reflection groups over finite fields to classify irreducible reflection fusion categories.

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