English

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 pq2pq^2, where pp and qq 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 \ZZ/3\ZZ\ZZ/3\ZZ-graded fusion categories, which are generalizations of the \ZZ/2\ZZ\ZZ/2\ZZ-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}
}