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Article Dans Une Revue Algebras and Representation Theory Année : 2016

Frobenius-Schur indicators for some fusion categories associated to symmetric and alternating groups

Résumé

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.

Dates et versions

hal-01122467 , version 1 (04-03-2015)

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Peter Schauenburg. Frobenius-Schur indicators for some fusion categories associated to symmetric and alternating groups. Algebras and Representation Theory, 2016, 19 (3), pp.645-656. ⟨10.1007/s10468-016-9593-8⟩. ⟨hal-01122467⟩
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