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RANK-FINITENESS FOR G-CROSSED BRAIDED FUSION CATEGORIES

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Abstract

We establish rank-finiteness for the class of G-crossed braided fusion categories, generalizing the recent result for modular categories and including the important case of braided fusion categories. This necessitates a study of slightly degenerate braided fusion categories and their centers, which are interesting for their own sake.

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Authors and Affiliations

  1. Department of Mathematics, The Ohio State University, Columbus, OH, 43202, USA

    C. JONES

  2. Mathematical Sciences Institute, Australian National University, Canberra, ACT, Australia

    S. MORRISON

  3. Department of Mathematics, University of New Hampshire, Durham, NH, 03824, USA

    D. NIKSHYCH

  4. Department of Mathematics, Texas A&M University, College Station, TX, 77840, USA

    E. C. ROWELL

Authors
  1. C. JONES
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  2. S. MORRISON
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  3. D. NIKSHYCH
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  4. E. C. ROWELL
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Correspondence to C. JONES.

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C. JONES is supported by NSF Grant DMS-1901082 and ARC grant DP140100732.

S. MORRISON is supported by ARC grants DP160103479 and FT170100019.

D. NIKSHYCH is Supported by NSF Grant DMS-1801198.

E. C. ROWELL is Supported by NSF DMS-1664359. This paper was initiated while ECR and DN were visiting CJ and SM at the Australian National University, and we gratefully acknowledge the support of that institution.

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JONES, C., MORRISON, S., NIKSHYCH, D. et al. RANK-FINITENESS FOR G-CROSSED BRAIDED FUSION CATEGORIES. Transformation Groups 26, 915–927 (2021). https://doi.org/10.1007/s00031-020-09576-2

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  • DOI: https://doi.org/10.1007/s00031-020-09576-2

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