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

2015/03/03 by Peter Schauenburg, Schauenburg, Peter · 1 citation
Mathematics · #16T05 #18D10 #20C15 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Rings and Algebras (math.RA) #math.QA #math.RA #msc:16T05 #msc:18D10 #msc:20C15

paper · pdf · doi:10.48550/arxiv.1503.01072

15 pages

arxiv created 2015/03/03 · openalex publication_date 2015/03/03 · arxiv updated 2015/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We calculate Frobenius-Schur indicator values for some fusion categories obtained from inclusions of finite groups H⊂ 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.

Cited by

• Weak Hopf algebras and the distribution of involutions in symmetric groups

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