On the classification of almost square-free modular categories

Jingcheng Dong; Sonia Natale

On the classification of almost square-free modular categories

Quantum Algebra 2017-11-10 v2

Authors: Jingcheng Dong , Sonia Natale

Abstract

Let $C$ be a modular category of Frobenius-Perron dimension $dq^n$ , where $q$ is a prime number and $d$ is a square-free integer. We show that if $q>2$ then $C$ is integral and nilpotent. In particular, $C$ is group-theoretical. In the general case, we describe the structure of $C$ in terms of equivariantizations of group-crossed braided fusion categories.

Keywords

tensor categories nilpotent groups frobenius algebra

Cite

@article{arxiv.1612.09112,
  title  = {On the classification of almost square-free modular categories},
  author = {Jingcheng Dong and Sonia Natale},
  journal= {arXiv preprint arXiv:1612.09112},
  year   = {2017}
}

Comments

final revised version. Main changes: Lemma 4.10 has been added, improving previous statement on dim dq^4. Also added Remark 4.9

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