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Extensions of Yang–Baxter sets Full article

Journal Theoretical and Mathematical Physics (Russian Federation)
ISSN: 0040-5779 , E-ISSN: 1573-9333
Output data Year: 2023, Volume: 215, Number: 2, Pages: 609-621 Pages count : 13 DOI: 10.1134/S0040577923050021
Tags Yang–Baxter equation, set-theoretic solution, quandle, Hopf algebra, extension of YangBaxter sets, product of Yang–Baxter sets, Drinfeld twist
Authors Bardakov V.G. 1,2,3 , Talalaev D.V. 4,5
Affiliations
1 Sobolev Institute of Mathematics, Novosibirsk, Russia
2 Novosibirsk State Agrarian University, Novosibirsk, Russia
3 Regional Scientific and Educational Mathematical Center of Tomsk State University, Dobrolyubova street, Tomsk, Russia
4 Lomonosov Moscow State University, Moscow, Russia
5 Demidov Yaroslavl State University, Yaroslavl, Russia

Funding (1)

1 Министерство науки и высшего образования РФ 075-02-2024-1437

Abstract: This paper is a first step in constructing the category of braided sets and its closest relative, the category of Yang-Baxter sets. Our main emphasis is on the construction of morphisms and extensions of Yang-Baxter sets. This problem is important for the possible constructions of new solutions of the Yang-Baxter equation and the braid equation. Our main result is the description of a family of solutions of the Yang-Baxter equation on B circle times C and on B x C, given two linear (set-theoretic) solutions (B, R-B) and (C, R-C) of the Yang-Baxter equation.
Cite: Bardakov V.G. , Talalaev D.V.
Extensions of Yang–Baxter sets
Theoretical and Mathematical Physics (Russian Federation). 2023. V.215. N2. P.609-621. DOI: 10.1134/S0040577923050021 WOS Scopus РИНЦ OpenAlex
Original: Бардаков В.Г. , Талалаев Д.В.
Расширения множеств Янга-Бакстера
Теоретическая и математическая физика. 2023. Т.215. №2. С.176-189. DOI: 10.4213/tmf10383 РИНЦ OpenAlex
Dates:
Submitted: Oct 13, 2022
Accepted: Dec 25, 2022
Published print: May 19, 2023
Published online: May 19, 2023
Identifiers:
Web of science: WOS:000992788200002
Scopus: 2-s2.0-85160916123
Elibrary: 61663049
OpenAlex: W4377101405
Citing:
DB Citing
Web of science 1
Scopus 2
OpenAlex 3
Elibrary 1
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