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

  • Paul Bruillard (a1), Cásar Galindo (a2), Seung-Moon Hong (a3), Yevgenia Kashina (a4), Deepak Naidu (a5), Sonia Natale (a6), Julia Yael Plavnik (a6) and Eric C. Rowell (a7)...

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.

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References

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Keywords

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

  • Paul Bruillard (a1), Cásar Galindo (a2), Seung-Moon Hong (a3), Yevgenia Kashina (a4), Deepak Naidu (a5), Sonia Natale (a6), Julia Yael Plavnik (a6) and Eric C. Rowell (a7)...

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