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Set-Theoretical Solutions of the -Simplex Equation. / Bardakov, V. G.; Chuzhinov, B. B.; Emelyanenkov, I. A. и др.
в: Siberian Advances in Mathematics, Том 34, № 1, 03.2024, стр. 1-40.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Set-Theoretical Solutions of the -Simplex Equation
AU - Bardakov, V. G.
AU - Chuzhinov, B. B.
AU - Emelyanenkov, I. A.
AU - Ivanov, M. E.
AU - Kozlovskaya, T. A.
AU - Leshkov, V. E.
N1 - The work was supported by the Russian Ministry of Science and Higher Education (agreement no. 075-02-2023-943).
PY - 2024/3
Y1 - 2024/3
N2 - The -simplex equation was introduced by Zamolodchikovas a generalization of the Yang–Baxter equation which becomes the -simplex equation in this terms. In the presentarticle, we suggest general approaches to construction of solutions of the -simplex equation, describe certain types ofsolutions, and introduce an operation that allows us to construct, under certain conditions,a solution of the -simplex equation from solutions of the-simplex equation and -simplex equation. We consider the tropicalizationof rational solutions and discuss its generalizations. We prove that a solution of the-simplex equation on can be constructed from solutions of this equationon and if is an extension of a group by a group. We also find solutions of the parametricYang–Baxter equation on with parameters in. We introduce ternary algebras for studyingthe 3-simplex equation and present examples of such algebras that provide us with solutions ofthe 3-simplex equation. We find all elementary verbal solutions of the 3-simplex equation on a freegroup.
AB - The -simplex equation was introduced by Zamolodchikovas a generalization of the Yang–Baxter equation which becomes the -simplex equation in this terms. In the presentarticle, we suggest general approaches to construction of solutions of the -simplex equation, describe certain types ofsolutions, and introduce an operation that allows us to construct, under certain conditions,a solution of the -simplex equation from solutions of the-simplex equation and -simplex equation. We consider the tropicalizationof rational solutions and discuss its generalizations. We prove that a solution of the-simplex equation on can be constructed from solutions of this equationon and if is an extension of a group by a group. We also find solutions of the parametricYang–Baxter equation on with parameters in. We introduce ternary algebras for studyingthe 3-simplex equation and present examples of such algebras that provide us with solutions ofthe 3-simplex equation. We find all elementary verbal solutions of the 3-simplex equation on a freegroup.
KW - 2-groupoid
KW - Yang–Baxter equation
KW - group extension
KW - groupoid
KW - n-simplex equation
KW - set-theoretical solution
KW - ternar
KW - ternoid
KW - tetrahedron equation
KW - tropicalization
KW - virtual braid group
UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85187428855&origin=inward&txGid=4456b3be010246e11b7dc629e12fa7a7
UR - https://www.mendeley.com/catalogue/cdb06eaf-6418-36e6-857a-cd7be5bbcff4/
U2 - 10.1134/S1055134424010012
DO - 10.1134/S1055134424010012
M3 - Article
VL - 34
SP - 1
EP - 40
JO - Siberian Advances in Mathematics
JF - Siberian Advances in Mathematics
SN - 1055-1344
IS - 1
ER -
ID: 61125007