Some properties of relative Rota–Baxter operators on groups

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 operator, semi-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

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

Submitted:	May 11, 2024
Accepted:	Sep 26, 2024
Published online:	Oct 19, 2024
Published print:	Feb 25, 2025

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

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OpenAlex	1
Scopus	1