Journal of Noncommutative Geometry

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Volume 8, Issue 4, 2014, pp. 1043–1060
DOI: 10.4171/JNCG/177

Published online: 2015-02-02

On weakly group-theoretical non-degenerate braided fusion categories

Sonia Natale[1]

(1) Universidad Nacional de Cordoba, Argentina

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 sucient 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: Braided fusion category, braided $G$-crossed fusion category, Tannakian category, Witt class, solvability

Natale Sonia: On weakly group-theoretical non-degenerate braided fusion categories. J. Noncommut. Geom. 8 (2014), 1043-1060. doi: 10.4171/JNCG/177