Some non-braided fusion categories of rank 3

Abstract

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.

arXiv comment18 pages, 7 figures, v2. Many expository improvements based on referee feedback, most notably to the proof of the main theorem and the section on pivotal structures. Fewer details are left to the reader. A new section outlines the structure of the proof of the main theorem and its relation to other results in the paper

References in corpus (1)

• Anyons in an exactly solved model and beyond

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