A Cuntz algebra approach to the classification of near-group categories
Operator Algebras
2015-12-31 v2 Category Theory
Quantum Algebra
Representation Theory
Abstract
We classify C near-group categories by using Vaughan Jones theory of subfactors and the Cuntz algebra endomorphisms. Our results show that there is a sharp contrast between two essentially different cases, integral and irrational cases. When the dimension of the unique non-invertible object is an integer, we obtain a complete classification list, and it turns out that such categories are always group theoretical. When it is irrational, we obtain explicit polynomial equations whose solutions completely classify the C near-group categories in this class.
Cite
@article{arxiv.1512.04288,
title = {A Cuntz algebra approach to the classification of near-group categories},
author = {Masaki Izumi},
journal= {arXiv preprint arXiv:1512.04288},
year = {2015}
}
Comments
135 pages.Theorem 2.2 and Theorem 13.3 are renewed and typographical errors are corrected