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Algebras and Representation Theory

, Volume 19, Issue 3, pp 645–656 | Cite as

Frobenius-Schur Indicators for Some Fusion Categories Associated to Symmetric and Alternating Groups

  • Peter SchauenburgEmail author
Article

Abstract

We calculate Frobenius-Schur indicator values for some fusion categories obtained from inclusions of finite groups \(H\subset G\), where more concretely G is symmetric or alternating, and H is a symmetric, alternating or cyclic group. Our work is strongly related to earlier results by Kashina-Mason-Montgomery, Jedwab-Montgomery, and Timmer for bismash product Hopf algebras obtained from exact factorizations of groups. We can generalize some of their results, settle some open questions and offer shorter proofs; this already pertains to the Hopf algebra case, while our results also cover fusion categories not associated to Hopf algebras.

Keywords

Fusion category Hopf algebra Frobenius-schur indicator 

Mathematical Subject Classification (2010)

18D10 16T05 20C15 

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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Institut de Mathématiques de Bourgogne, UMR5584 CNRSUniversité Bourgogne Franche-ComtéDijonFrance

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