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Integral Modular Categories of Frobenius-Perron Dimension pq n

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Abstract

Integral modular categories of Frobenius-Perron dimension pq n, where p and q are primes, are considered. It is already known that such categories are group-theoretical in the cases of 0 ≤ n ≤ 4. In the general case we determine that these categories are either group-theoretical or contain a Tannakian subcategory of dimension q i for i > 1. We then show that all integral modular categories \(\mathcal {C}\) with \(\text {FPdim}(\mathcal {C})=pq^{5}\) are group-theoretical, and, if in addition p < q, all with \(\text {FPdim}(\mathcal {C})=pq^{6}\) or pq 7 are group-theoretical. In the process we generalize an existing criterion for an integral modular category to be group-theoretical.

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Authors and Affiliations

  1. College of Engineering, Nanjing Agricultural University, Nanjing, 210031, China

    Jingcheng Dong

  2. Department of Mathematics, University of Southern California, Los Angeles, CA, 90089, USA

    Henry Tucker

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  1. Jingcheng Dong
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  2. Henry Tucker
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Correspondence to Jingcheng Dong.

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Presented by Kenneth Goodearl.

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Dong, J., Tucker, H. Integral Modular Categories of Frobenius-Perron Dimension pq n . Algebr Represent Theor 19, 33–46 (2016). https://doi.org/10.1007/s10468-015-9560-9

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  • DOI: https://doi.org/10.1007/s10468-015-9560-9

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