Pivotal fusion categories of rank 3 (with an Appendix written jointly with Dmitri Nikshych)

Abstract

We classify all fusion categories of rank 3 that admit a pivotal structure over an algebraically closed field of characteristic zero. Also in the Appendix (joint with D.Nikshych) we give some restrictions on Grothendieck rings of near-group categories.

27 pages

References in corpus (4)

• The classification of subfactors of index at most 5
• Cyclotomic integers, fusion categories, and subfactors
• The fusion algebra of bimodule categories
• On braided near-group categories

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• On twisted Verlinde formulae for modular categories
• A complete classification of unitary fusion categories tensor generated by an object of dimension $\frac{1+\sqrt{5}}{2}$
• Non-trivially graded self-dual fusion categories of rank $4$
• The monoidal center and the character algebra