On weakly group-theoretical non-degenerate braided fusion categories

NATALE, S.

Viena

Workshop; Modern trends in topological quantum field theory; 2014

Erwin Schrödinger Institute

A fusion category is called weakly group-theoretical if it is tensor Morita equivalent to a nilpotent fusion category. It is conjectured that every fusion category of integer Frobenius-Perron dimension is weakly group-theoretical. We shall present a result concerning the class of a braided non-degenerate weakly group-theoretical fusion category in the Witt group introduced recently by Davydov, Müger, Nikshych and Ostrik. We shall 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.