Rota—Baxter groups, skew left braces, and the Yang—Baxter equation Full article
| Journal |
Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X |
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| Output data | Year: 2022, Volume: 596, Pages: 328-351 Pages count : 24 DOI: 10.1016/j.jalgebra.2021.12.036 | ||||||||
| Tags | Rota—Baxter group; Rota—Baxter operator; Skew left brace; Yang—Baxter equation | ||||||||
| Authors |
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| Affiliations |
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Funding (2)
| 1 | Russian Science Foundation | 21-11-00286 |
| 2 | Министерство науки и высшего образования РФ | 075-02-2020-1479/1 |
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.
Cite:
Bardakov V.G.
, Gubarev V.
Rota—Baxter groups, skew left braces, and the Yang—Baxter equation
Journal of Algebra. 2022. V.596. P.328-351. DOI: 10.1016/j.jalgebra.2021.12.036 WOS Scopus РИНЦ OpenAlex
Rota—Baxter groups, skew left braces, and the Yang—Baxter equation
Journal of Algebra. 2022. V.596. P.328-351. DOI: 10.1016/j.jalgebra.2021.12.036 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | May 22, 2021 |
| Published online: | Jan 6, 2022 |
Identifiers:
| Web of science: | WOS:000794858600013 |
| Scopus: | 2-s2.0-85123361818 |
| Elibrary: | 48145139 |
| OpenAlex: | W4205495576 |