Classification of integral modular categories of Frobenius–Perron dimension pq4 and p2q2
Date
2014Author
Bruillard, Paul
Galindo Martínez, César Neyit
Hong, Seung-Moon
Kashina, Yevgenia
Naidu, Deepak
Natale, Sonia Luján
Plavnik, Julia Yael
Rowell, Eric C.
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We classify integral modular categories of dimension pq4 and p2q2, where p and q are distinct primes. We show that such categories are always group-theoretical, except for categories of dimension 4q2. In these cases there are well-known examples of non-group-theoretical categories, coming from centers of Tambara–Yamagami categories and quantum groups. We show that a non-group-theoretical integral modular category of dimension 4q2 is either equivalent to one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising from a certain quantum group.