10/05/2018, Room 27, FaMAF

On the structure of weakly group-theoretical braided fusion categories.

Speaker: Sonia Natale

Abstract:
In this talk, we will review the definition of the core of a braided fusion category, introduced by Drinfeld, Gelaki, Nikshych and Ostrik, and its relation with G-crossed braided fusion categories, where G is a finite group, introduced by Turaev. Our main result is the determination of such core in the case of a weakly group-theoretical fusion category, according to the definition of Etingof, Nikshych and Ostrik: more precisely, we shall prove that in this case, the core is a Deligne product $\B \boxtimes \D$, where $\D$ is a pointed weakly anisotropic braided fusion category and $\B$ is either trivial or is equivalent to an Ising category. Some applications will be presented, such as a characterization of the solvability of a group-theoretical braided fusion category in terms of Tannakian subcategories, and a result about the structure of integral modular categories all of whose simple objects have Frobenius-Perron dimension at most 2.