Classification of Integral Modular Categories of Frobenius–Perron Dimension pq 4 and p 2 q 2

Bruillard, Paul ; Galindo, Cásar ; Hong, Seung-Moon ; Kashina, Yevgenia ; Naidu, Deepak ; Natale, Sonia ; Plavnik, Julia Yael ; Rowell, Eric C.

Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 721-734

Résumé

We classify integral modular categories of dimension $p{{q}^{4}}$ and ${{p}^{2}}{{q}^{2}}$ , where $p$ and $q$ are distinct primes. We show that such categories are always group-theoretical, except for categories of dimension $4{{q}^{2}}$ . 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-grouptheoretical integral modular category of dimension $4{{q}^{2}}$ is either equivalent to one of these well-known examples or is of dimension 36 and is twist-equivalent to fusion categories arising froma certain quantum group.

Détail

DOI : 10.4153/CMB-2013-042-6

Mots-clés : 18D10, modular categories, fusion categories

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