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arXiv · 1704.03523

The core of a weakly group-theoretical braided fusion category

Sonia Natale
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Abstract

We show that the core of a weakly group-theoretical braided fusion category $\C$ is equivalent as a braided fusion category to a tensor product $\B \boxtimes \D$, where $\D$ is a pointed weakly anisotropic braided fusion category, and $\B \cong \vect$ or $\B$ is an Ising braided category. In particular, if $\C$ is integral, then its core is a pointed weakly anisotropic braided fusion category. As an application we give a characterization of the solvability of a weakly group-theoretical braided fusion category. We also prove that an integral modular category all of whose simple objects have Frobenius-Perron dimension at most 2 is necessarily group-theoretical.

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Sonia Natale. 2017-04-11. The core of a weakly group-theoretical braided fusion category. https://arxiv.org/abs/1704.03523

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