Classification of integral modular categories of Frobenius-Perron dimension $pq^4$ and $p^2q^2$

BRUILLARD, P.; HONG, S. M.; GALINDO, C.; KASHINA, Y.; NAIDU, D.; NATALE, S.; PLAVNIK, J.; ROWELL, E.

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES

CANADIAN MATHEMATICAL SOC

Lugar: Vancouver; Año: 2014 vol. 57 p. 721 - 734

0008-4395

We classify integral modular categories of dimension $pq^4$ and $p^2q^2$ where p andq are distinct primes. We show that such categories are always group-theoretical except forcategories of dimension $4q^2$. In these cases there are well-known examples of non-grouptheoretical categories, coming from centers of Tambara-Yamagami categories and quantumgroups. We show that a non-group-theoretical integral modular category of dimension $4q^2$is equivalent to either one of these well-known examples or is of dimension 36 and is twistequivalentto fusion categories arising from a certain quantum group.