On weakly group-theoretical non-degenerate braided fusion categories
Abstract
We show that the Witt class of a weakly group-theoretical non-degenerate braided fusion category belongs to the subgroup generated by classes of non-degenerate pointed braided fusion categories and Ising braided categories. This applies in particular to solvable non-degenerate braided fusion categories. We also give some sufficient conditions for a braided fusion category to be weakly group-theoretical or solvable in terms of the factorization of its Frobenius-Perron dimension and the Frobenius-Perron dimensions of its simple objects. As an application, we prove that every non-degenerate braided fusion category whose Frobenius-Perron dimension is a natural number less than 1800, or an odd natural number less than 33075, is weakly group-theoretical.
Keywords
Cite
@article{arxiv.1301.6078,
title = {On weakly group-theoretical non-degenerate braided fusion categories},
author = {Sonia Natale},
journal= {arXiv preprint arXiv:1301.6078},
year = {2013}
}
Comments
17 pages, amslatex