Sciact
  • EN
  • RU

Some properties of relative Rota–Baxter operators on groups Full article

Journal Communications in Algebra
ISSN: 0092-7872 , E-ISSN: 1532-4125
Output data Year: 2025, Volume: 53, Number: 4, Pages: 1453-1469 Pages count : 17 DOI: 10.1080/00927872.2024.2413691
Tags Group nilpotent group relative Rota–Baxter operator Rota–Baxter operatorsemi-direct product skew brace Yang–Baxter equation
Authors Bardakov V.G. 1,2 , Kozlovskaya T.A. 3 , Sololov P.P. 4 , Zimireva K.V. 4 , Zonov M.N. 1
Affiliations
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

Funding (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

Abstract: 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.
Cite: 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
Dates:
Submitted: May 11, 2024
Accepted: Sep 26, 2024
Published online: Oct 19, 2024
Published print: Feb 25, 2025
Identifiers:
Web of science: WOS:001336271000001
Scopus: 2-s2.0-85207295439
OpenAlex: W4403560740
Citing: Пока нет цитирований
Altmetrics: