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Some properties of relative Rota–Baxter operators on groups. / Bardakov, V. G.; Kozlovskaya, T. A.; Sololov, P. P. et al.

In: Communications in Algebra, 29.10.2024.

Research output: Contribution to journal › Article › peer-review

Harvard

Bardakov, VG, Kozlovskaya, TA, Sololov, PP, Zimireva, KV & Zonov, MN 2024, 'Some properties of relative Rota–Baxter operators on groups', Communications in Algebra. https://doi.org/10.1080/00927872.2024.2413691

APA

Bardakov, V. G., Kozlovskaya, T. A., Sololov, P. P., Zimireva, K. V., & Zonov, M. N. (2024). Some properties of relative Rota–Baxter operators on groups. Communications in Algebra. https://doi.org/10.1080/00927872.2024.2413691

Vancouver

Bardakov VG, Kozlovskaya TA, Sololov PP, Zimireva KV, Zonov MN. Some properties of relative Rota–Baxter operators on groups. Communications in Algebra. 2024 Oct 29. doi: 10.1080/00927872.2024.2413691

Author

Bardakov, V. G. ; Kozlovskaya, T. A. ; Sololov, P. P. et al. / Some properties of relative Rota–Baxter operators on groups. In: Communications in Algebra. 2024.

BibTeX

@article{fe416646350d43b18e56ff4a0d8f4d52,
title = "Some properties of relative Rota–Baxter operators on groups",
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.",
keywords = "Group, Rota–Baxter operator, Yang–Baxter equation, nilpotent group, relative Rota–Baxter operator, semi-direct product, skew brace",
author = "Bardakov, {V. G.} and Kozlovskaya, {T. A.} and Sololov, {P. P.} and Zimireva, {K. V.} and Zonov, {M. N.}",
note = "The first author was supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2024-1437). The remaining authors were supported by the Theoretical Physics and Mathematics Advancement Foundation BASIS No 23-7-2-14-1.",
year = "2024",
month = oct,
day = "29",
doi = "10.1080/00927872.2024.2413691",
language = "English",
journal = "Communications in Algebra",
issn = "0092-7872",
publisher = "Taylor and Francis Ltd.",

}

RIS

TY - JOUR

T1 - Some properties of relative Rota–Baxter operators on groups

AU - Bardakov, V. G.

AU - Kozlovskaya, T. A.

AU - Sololov, P. P.

AU - Zimireva, K. V.

AU - Zonov, M. N.

N1 - The first author was supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2024-1437). The remaining authors were supported by the Theoretical Physics and Mathematics Advancement Foundation BASIS No 23-7-2-14-1.

PY - 2024/10/29

Y1 - 2024/10/29

N2 - 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.

AB - 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.

KW - Group

KW - Rota–Baxter operator

KW - Yang–Baxter equation

KW - nilpotent group

KW - relative Rota–Baxter operator

KW - semi-direct product

KW - skew brace

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UR - https://www.webofscience.com/wos/woscc/full-record/WOS:001336271000001

UR - https://www.mendeley.com/catalogue/68c972c0-ec2f-3311-a647-3d8ae9ff7cb6/

U2 - 10.1080/00927872.2024.2413691

DO - 10.1080/00927872.2024.2413691

M3 - Article

JO - Communications in Algebra

JF - Communications in Algebra

SN - 0092-7872

ER -

ID: 61204756