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Some Notes on Higher Frobenius–Schur Indicators of the Regular Representations for Matched Pairs of Groups

Author

Listed:
  • Chenfei Mao

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China)

  • Kangqiao Li

    (School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China)

Abstract

The notion of matched pair ( F , G , ▹ , ◃ ) of finite groups was introduced by Takeuchi in 1981, which is equivalent to a factorization of the group F ⋈ G . We find in this paper some sufficient conditions when equations ν m ( F ⋈ G ) = ν m ( F ) ν m ( G ) for all m ≥ 0 imply that F ⋈ G is the external direct product of F × G , where ν m denotes m -th indicator of the regular representation of a finite group. A comparison with indicators of bismash product Hopf algebras C G # C F is also mentioned.

Suggested Citation

  • Chenfei Mao & Kangqiao Li, 2024. "Some Notes on Higher Frobenius–Schur Indicators of the Regular Representations for Matched Pairs of Groups," Mathematics, MDPI, vol. 12(22), pages 1-12, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3479-:d:1516070
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