Some Notes on Higher Frobenius–Schur Indicators of the Regular Representations for Matched Pairs of Groups
Year: 2024
Type: article
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 νm(F⋈G)=νm(F)νm(G) for all m≥0 imply that F⋈G is the external direct product of F×G, where νm denotes m-th indicator of the regular representation of a finite group. A comparison with indicators of bismash product Hopf algebras CG#CF is also mentioned.
Source: Mathematics
DOI: 10.3390/math12223479
Authors: Chenfei Mao, Kangqiao Li
Institution: Hangzhou Normal University
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
Award: G499639023
OpenAlex ID: W4404141318