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A Higher Frobenius–Schur Indicator Formula for Group-Theoretical Fusion Categories

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An Erratum to this article was published on 27 October 2016

Abstract

Group-theoretical fusion categories are defined by data concerning finite groups and their cohomology: a finite group G endowed with a three-cocycle ω, and a subgroup \({H\subset G}\) endowed with a two-cochain whose coboundary is the restriction of ω. The objects of the category are G-graded vector spaces with suitably twisted \({H}\)-actions; the associativity of tensor products is controlled by ω. Simple objects are parametrized in terms of projective representations of finite groups, namely of the stabilizers in H of right H-cosets in G, with respect to two-cocycles defined by the initial data. We derive and study general formulas that express the higher Frobenius–Schur indicators of simple objects in a group-theoretical fusion category in terms of the group-theoretical and cohomological data defining the category and describing its simples.

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Authors and Affiliations

  1. Institut de Mathématiques de Bourgogne, UMR 5584 CNRS, Université Bourgogne Franche-Comté, 21000, Dijon, France

    Peter Schauenburg

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  1. Peter Schauenburg
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Correspondence to Peter Schauenburg.

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Communicated by Y. Kawahigashi

Research partially supported through a FABER Grant by the Conseil régional de Bourgogne.

An erratum to this article can be found at http://dx.doi.org/10.1007/s00220-016-2770-0.

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Schauenburg, P. A Higher Frobenius–Schur Indicator Formula for Group-Theoretical Fusion Categories. Commun. Math. Phys. 340, 833–849 (2015). https://doi.org/10.1007/s00220-015-2437-2

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