On the classification of almost square-free modular categories

Abstract

Let $C$ be a modular category of Frobenius-Perron dimension $d{q}^n$, where $q$ is a prime number and $d$ is a square-free integer. We show that if $q>2$ then $C$ is integral and nilpotent. In particular, $C$ is group-theoretical. In the general case, we describe the structure of $C$ in terms of equivariantizations of group-crossed braided fusion categories.

final revised version. Main changes: Lemma 4.10 has been added, improving previous statement on dim dq^4. Also added Remark 4.9

References in corpus (1)

• Generalized Tambara-Yamagami categories

Cited by in corpus (1)

• On semisimple quasitriangular Hopf algebras of dimension $d{q}^n$