Rota—Baxter groups, skew left braces, and the Yang—Baxter equation

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Rota—Baxter groups, skew left braces, and the Yang—Baxter equation. / Bardakov, Valeriy G.; Gubarev, Vsevolod.

In: Journal of Algebra, Vol. 596, 15.04.2022, p. 328-351.

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

BibTeX

@article{83e4177520b942b092059d5addad4431,

title = "Rota—Baxter groups, skew left braces, and the Yang—Baxter equation",

abstract = "Braces were introduced by W. Rump in 2006 as an algebraic system related to the quantum Yang—Baxter equation. In 2017, L. Guarnieri and L. Vendramin defined for the same purposes a more general notion of a skew left brace. In 2020, L. Guo, H. Lang and Y. Sheng gave a definition of what is a Rota—Baxter operator on a group. We connect these two notions as follows. It is shown that every Rota—Baxter group gives rise to a skew left brace. Moreover, every skew left brace can be injectively embedded into a Rota—Baxter group. When the additive group of a skew left brace is complete, then this brace is induced by a Rota—Baxter group. We interpret some notions of the theory of skew left braces in terms of Rota—Baxter operators.",

keywords = "Rota—Baxter group, Rota—Baxter operator, Skew left brace, Yang—Baxter equation",

author = "Bardakov, {Valeriy G.} and Vsevolod Gubarev",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier Inc.",

year = "2022",

month = apr,

day = "15",

doi = "10.1016/j.jalgebra.2021.12.036",

language = "English",

volume = "596",

pages = "328--351",

journal = "Journal of Algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Rota—Baxter groups, skew left braces, and the Yang—Baxter equation

AU - Bardakov, Valeriy G.

AU - Gubarev, Vsevolod

PY - 2022/4/15

Y1 - 2022/4/15

N2 - Braces were introduced by W. Rump in 2006 as an algebraic system related to the quantum Yang—Baxter equation. In 2017, L. Guarnieri and L. Vendramin defined for the same purposes a more general notion of a skew left brace. In 2020, L. Guo, H. Lang and Y. Sheng gave a definition of what is a Rota—Baxter operator on a group. We connect these two notions as follows. It is shown that every Rota—Baxter group gives rise to a skew left brace. Moreover, every skew left brace can be injectively embedded into a Rota—Baxter group. When the additive group of a skew left brace is complete, then this brace is induced by a Rota—Baxter group. We interpret some notions of the theory of skew left braces in terms of Rota—Baxter operators.

AB - Braces were introduced by W. Rump in 2006 as an algebraic system related to the quantum Yang—Baxter equation. In 2017, L. Guarnieri and L. Vendramin defined for the same purposes a more general notion of a skew left brace. In 2020, L. Guo, H. Lang and Y. Sheng gave a definition of what is a Rota—Baxter operator on a group. We connect these two notions as follows. It is shown that every Rota—Baxter group gives rise to a skew left brace. Moreover, every skew left brace can be injectively embedded into a Rota—Baxter group. When the additive group of a skew left brace is complete, then this brace is induced by a Rota—Baxter group. We interpret some notions of the theory of skew left braces in terms of Rota—Baxter operators.

KW - Rota—Baxter group

KW - Rota—Baxter operator

KW - Skew left brace

KW - Yang—Baxter equation

UR - http://www.scopus.com/inward/record.url?scp=85123361818&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2021.12.036

DO - 10.1016/j.jalgebra.2021.12.036

M3 - Article

AN - SCOPUS:85123361818

VL - 596

SP - 328

EP - 351

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

ID: 35386203