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

Abstract

Group-theoretical fusion categories are defined by data concerning finite groups and their cohomology: A finite group $G$ endowed with a three-cocycle $\omega$, and a subgroup $H\subset G$ endowed with a two-cochain whose coboundary is the restriction of $\omega$. The objects of the category are $G$-graded vector spaces with suitably twisted $H$-actions; the associativity of tensor products is controlled by $\omega$. 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.

21 pages

References in corpus (2)

• Central Invariants and Frobenius-Schur Indicators for Semisimple Quasi-Hopf Algebras
• On the Gauge Equivalence of Twisted Quantum Doubles of Elementary Abelian and Extra-Special 2-Groups

Cited by in corpus (1)

• Algebraic realization of noncommutative near-group fusion categories