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Algebras and Representation Theory

, Volume 21, Issue 6, pp 1353–1368 | Cite as

On the Classification of Almost Square-Free Modular Categories

  • Jingcheng Dong
  • Sonia Natale
Article
  • 16 Downloads

Abstract

Let \(\mathcal {C}\) be a modular category of Frobenius-Perron dimension d q n , where q > 2 is a prime number and d is a square-free integer. We show that \(\mathcal {C}\) must be integral and nilpotent and therefore group-theoretical. In the case where q = 2, we describe the structure of \(\mathcal {C}\) in terms of equivariantizations of group-crossed braided fusion categories.

Keywords

Braided fusion category Modular category Group-theoretical fusion category Braided G-crossed fusion category Tannakian category 

Mathematics Subject Classification (2010)

18D10 16T05 

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Notes

Acknowledgements

The first author was partially supported by the Fundamental Research Funds for the Central Universities (KYZ201564), the Natural Science Foundation of China (11201231) and the Qing Lan Project. The second author was partially supported by CONICET and SeCYT–UNC.

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Authors and Affiliations

  1. 1.College of EngineeringNanjing Agricultural UniversityNanjingChina
  2. 2.Facultad de Matemática, Astronomía y FísicaUniversidad Nacional de Córdoba, CIEM – CONICET, Ciudad UniversitariaCórdobaArgentina

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