Communications in Mathematical Physics

, Volume 340, Issue 2, pp 833–849 | Cite as

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

Article

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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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Institut de Mathématiques de Bourgogne, UMR 5584 CNRSUniversité Bourgogne Franche-ComtéDijonFrance

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