2013/01/25 by Sonia Natale, Natale, Sonia
Mathematics · Physics and Astronomy · #18D10 #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #Quantum Algebra (math.QA) #math.QA #msc:18D10
paper · pdf · doi:10.48550/arxiv.1301.6078
17 pages, amslatex
arxiv created 2013/01/25 · openalex publication_date 2013/01/25 · arxiv updated 2013/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.