On the classification of certain fusion categories
Quantum Algebra
2010-03-23 v2 Category Theory
Abstract
We advance the classification of fusion categories in two directions. Firstly, we completely classify integral fusion categories -- and consequently, semi-simple Hopf algebras -- of dimension , where and are distinct primes. This case is especially interesting because it is the simplest class of dimensions where not all integral fusion categories are group-theoretical. Secondly, we classify a certain family of -graded fusion categories, which are generalizations of the -graded Tambara-Yamagami categories. Our proofs are based on the recently developed theory of extensions of fusion categories.
Keywords
Cite
@article{arxiv.0812.1603,
title = {On the classification of certain fusion categories},
author = {David Jordan and Eric Larson},
journal= {arXiv preprint arXiv:0812.1603},
year = {2010}
}