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.
Keywords
Cite
@article{arxiv.0704.0208,
title = {Some non-braided fusion categories of rank 3},
author = {Tobias J. Hagge and Seung-Moon Hong},
journal= {arXiv preprint arXiv:0704.0208},
year = {2007}
}
Comments
18 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