Set-Theoretical Solutions of the n-Simplex Equation Full article
| Journal |
Siberian Advances in Mathematics
ISSN: 1055-1344 , E-ISSN: 1934-8126 |
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| Output data | Year: 2024, Volume: 34, Number: 1, Pages: 1-40 Pages count : 40 DOI: 10.1134/s1055134424010012 | ||||||
| Tags | Yang-Baxter equation, tetrahedral equation, n-simplex equation, settheoretiс solution, groupoid, 2-groupoid, ternary, ternoid, group extension, virtual braid group. | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Министерство науки и высшего образования РФ | 075-02-2024-1437 |
Abstract:
The n-simplex equation was introduced by Zamolodchikov as a generalization of the Yang–Baxter equation which becomes the 2-simplex equation in this terms. In the present article, we suggest general approaches to construction of solutions of the n-simplex equation, describe certain types of solutions, and introduce an operation that allows us to construct, under certain conditions, a solution of the (n + m + k)-simplex equation from solutions of the (n + k)simplex equation and (m + k)-simplex equation. We consider the tropicalization of rational solutions and discuss its generalizations. We prove that a solution of the n-simplex equation on G can be constructed from solutions of this equation on H and K if G is an extension of a group H by a group K. We also find solutions of the parametric Yang–Baxter equation on H with parameters in K. We introduce ternary algebras for studying the 3-simplex equation and present examples of such algebras that provide us with solutions of the 3-simplexequation. We find all elementary verbal solutions of the 3-simplex equation on a free group.
Cite:
Bardakov V.G.
, Chuzhinov B.
, Emel'yanenkov I.А.
, Ivanov M.
, Kozlovskaya T.A.
, Leshkov V.
Set-Theoretical Solutions of the n-Simplex Equation
Siberian Advances in Mathematics. 2024. V.34. N1. P.1-40. DOI: 10.1134/s1055134424010012 Scopus РИНЦ OpenAlex
Set-Theoretical Solutions of the n-Simplex Equation
Siberian Advances in Mathematics. 2024. V.34. N1. P.1-40. DOI: 10.1134/s1055134424010012 Scopus РИНЦ OpenAlex
Original:
Бардаков В.Г.
, Чужинов Б.Б.
, Емельяненков И.А.
, Иванов М.Э.
, Козловская Т.А.
, Лешков В.Е.
Теоретико-множественные решения уравнений n-симплексов
Математические труды. 2024. Т.27. №1. С.5-72. DOI: 10.25205/1560-750X-2024-27-1-5-72 РИНЦ
Теоретико-множественные решения уравнений n-симплексов
Математические труды. 2024. Т.27. №1. С.5-72. DOI: 10.25205/1560-750X-2024-27-1-5-72 РИНЦ
Dates:
| Submitted: | Nov 27, 2023 |
| Accepted: | Dec 26, 2023 |
| Published print: | Mar 11, 2024 |
| Published online: | Mar 11, 2024 |
Identifiers:
| Scopus: | 2-s2.0-85187428855 |
| Elibrary: | 66305128 |
| OpenAlex: | W4392659845 |