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Rota-Baxter Operators on Dihedral and Alternating Groups Научная публикация

Журнал

Advances in Group Theory and Applications
ISSN: 2499-1287

Вых. Данные

Год: 2026, Том: 23, Страницы: 27-62 Страниц : 36 DOI: 10.32037/agta-2026-003

Ключевые слова

Rota–Baxter operator; Rota–Baxter group; dihedral group; alternating group

Авторы

Galt Alexey ^1,2 , Gubarev Vsevolod ^1,2

Организации

1	Novosibirsk State University
2	Sobolev Institute of Mathematics

Информация о финансировании (1)

Российский научный фонд

23-71-10005

Rota–Baxter operators on algebras, which appeared in 1960, have connections with different versions of the Yang–Baxter equation, pre- and postalgebras, double Poisson algebras, etc. In 2020, the notion of Rota–Baxter operator on a group was defined by L. Guo, H. Lang, Yu. Sheng. In 2023, V. Bardakov and the second author showed that all Rota–Baxter operators on simple sporadic groups are splitting, i.e. they are defined via exact factorizations. In this work, we clarify for which n there exist non-splitting Rota–Baxter operators on the alternating group An. For the corresponding n, we describe all non-splitting Rota–Baxter operators on An. Besides, we describe Rota–Baxter operators on dihedral groups D2n providing the general construction which lies behind all non-splitting Rota–Baxter operators on An and D2n.

Galt A. , Gubarev V.
Rota-Baxter Operators on Dihedral and Alternating Groups
Advances in Group Theory and Applications. 2026. V.23. P.27-62. DOI: 10.32037/agta-2026-003

Поступила в редакцию:	27 апр. 2024 г.
Принята к публикации:	14 окт. 2024 г.
Опубликована в печати:	1 июн. 2026 г.

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