Classification of Integral Modular Categories of Frobenius–Perron Dimension pq 4 and p 2 q 2
Classification of Integral Modular Categories of Frobenius–Perron Dimension pq 4 and p 2 q 2
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DOI：
10.4153/cmb-2013-042-6
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发表时间：
2013-03
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通讯作者：
P. Bruillard;C. Galindo;Seung-Moon Hong;Yevgenia Kashina;D. Naidu;S. Natale;Julia Yael Plavnik;E. Rowell
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文献类型：
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作者：
P. Bruillard;C. Galindo;Seung-Moon Hong;Yevgenia Kashina;D. Naidu;S. Natale;Julia Yael Plavnik;E. Rowell
Abstract 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.
Abstract 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.