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Some properties of relative Rota–Baxter operators on groups Научная публикация

Журнал

Communications in Algebra
ISSN: 0092-7872 , E-ISSN: 1532-4125

Вых. Данные

Год: 2025, Том: 53, Номер: 4, Страницы: 1453-1469 Страниц : 17 DOI: 10.1080/00927872.2024.2413691

Ключевые слова

Group, nilpotent group, relative Rota–Baxter operator, Rota–Baxter operator, semi-direct product, skew brace, Yang–Baxter equation

Авторы

Bardakov V.G. ^1,2 , Kozlovskaya T.A. ³ , Sololov P.P. ⁴ , Zimireva K.V. ⁴ , Zonov M.N. ¹

Организации

1	Sobolev Institute of Mathematics, Novosibirsk, Russia
2	Tomsk State University, Tomsk, Russia
3	Regional Scientific and Educational Mathematical Center of Tomsk State University, Tomsk, Russia
4	Novosibirsk State University, Novosibirsk, Russia

Информация о финансировании (2)

1	Министерство науки и высшего образования РФ	075-02-2024-1437
2	Фонд развития теоретической физики и математики «БАЗИС»	23-7-2-14-1

We find connection between relative Rota–Baxter operators and usual Rota–Baxter operators. We prove that any relative Rota–Baxter operator on a group H with respect to (Formula presented.) defines a Rota–Baxter operator on the semi-direct product (Formula presented.). On the other side, we give condition under which a Rota–Baxter operator on the semi-direct product (Formula presented.) defines a relative Rota–Baxter operator on H with respect to (Formula presented.). We introduce homomorphic post-groups and find their connection with λ-homomorphic skew left braces. Further, we construct post-group on arbitrary group and a family of post-groups which depends on integer parameter on any two-step nilpotent group. We find all verbal solutions of the quantum Yang-Baxter equation on two-step nilpotent group.

Bardakov V.G. , Kozlovskaya T.A. , Sololov P.P. , Zimireva K.V. , Zonov M.N.
Some properties of relative Rota–Baxter operators on groups
Communications in Algebra. 2025. V.53. N4. P.1453-1469. DOI: 10.1080/00927872.2024.2413691 WOS Scopus OpenAlex

Поступила в редакцию:	11 мая 2024 г.
Принята к публикации:	26 сент. 2024 г.
Опубликована online:	19 окт. 2024 г.
Опубликована в печати:	25 февр. 2025 г.

Web of science:	WOS:001336271000001
Scopus:	2-s2.0-86000426288
OpenAlex:	W4403560740

БД	Цитирований
Scopus	1