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Some non-braided fusion categories of rank 3 · Around

2007

Some non-braided fusion categories of rank 3

Hagge, Tobias J., Hong, Seung-Moon

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We classify all fusion categories for a given set of fusion rules with three simple object types.

If a conjecture of Ostrik is true, our classification completes the classification of fusion categories with three simple object types.
To facilitate the discussion we describe a convenient, concrete and useful variation of graphical calculus for fusion categories, discuss pivotality and sphericity in this framework, and give a short and elementary re-proof of the fact that the quadruple dual functor is naturally isomorphic to the identity.

Built on

A theoretical basis for the reduction of polynomials to canonical forms
Bruno Buchberger · 1976
Earlier work this paper cites.
Categories for the Working Mathematician, Second Edition
Saunders Mac Lane · 1978
Earlier work this paper cites.
Quantum groups, quantum categories, and quantum field theory
J. Frohlich and T. Kerler · 1993
Earlier work this paper cites.
Reconstructing monoidal categories
Kazhdan and Hans Wenzl · 1993
Earlier work this paper cites.

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Then

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