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

Chenfei Mao and Kangqiao Li ()
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Chenfei Mao: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China
Kangqiao Li: School of Mathematics, Hangzhou Normal University, Hangzhou 311121, China

Mathematics, 2024, vol. 12, issue 22, 1-12

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.

Keywords: finite group; higher Frobenius–Schur indicator; matched pair of groups; factorizable group; direct product (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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