V. V. Sokolov, “Classification of constant solutions of the associative Yang–Baxter equation on $\operatorname{Mat}_3$”, TMF, 176:3 (2013), 385–392; Theoret. and Math. Phys., 176:3 (2013), 1156

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Teoreticheskaya i Matematicheskaya Fizika, 2013, Volume 176, Number 3, Pages 385–392
DOI: https://doi.org/10.4213/tmf8467 (Mi tmf8467)

This article is cited in 13 scientific papers (total in 13 papers)

Classification of constant solutions of the associative Yang–Baxter equation on

{Mat}_{3}

$\operatorname{Mat}_3$

V. V. Sokolov

Landau Institute for Theoretical Physics, Moscow, Russia

Full-text PDF (377 kB) Citations (13)

References:

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DOI: https://doi.org/10.4213/tmf8467

Abstract: We find all nonequivalent constant solutions of the classical associative Yang–Baxter equation for

{Mat}_{3}

$\operatorname{Mat}_3$ . New examples found in the classification yield the corresponding Poisson brackets on traces, double Poisson brackets on a free associative algebra with three generators, and anti-Frobenius associative algebras.

Keywords: associative Yang–Baxter equation, constant solution, classification.

Received: 06.01.2013

English version:
Theoretical and Mathematical Physics, 2013, Volume 176, Issue 3, Pages 1156–1162
DOI: https://doi.org/10.1007/s11232-013-0096-z

Bibliographic databases:

Document Type: Article

Language: Russian

Citation: V. V. Sokolov, “Classification of constant solutions of the associative Yang–Baxter equation on

{Mat}_{3}

$\operatorname{Mat}_3$ ”, TMF, 176:3 (2013), 385–392; Theoret. and Math. Phys., 176:3 (2013), 1156–1162

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/tmf8467

https://doi.org/10.4213/tmf8467

https://www.mathnet.ru/eng/tmf/v176/i3/p385

This publication is cited in the following 13 articles:

Vsevolod Gubarev, “Rota–Baxter Operators of Weight Zero on Upper-Triangular Matrices of Order Three”, Mediterr. J. Math., 21:7 (2024)
Valeriy G. Bardakov, Igor M. Nikonov, Viktor N. Zhelaybin, “Lie Rota–Baxter operators on the Sweedler algebra H4”, Int. J. Algebra Comput., 34:08 (2024), 1159
Goncharov M., Gubarev V., “Rota-Baxter Operators of Nonzero Weight on the Matrix Algebra of Order Three”, Linear Multilinear Algebra, 70:6 (2022), 1055–1080
M. E. Goncharov, D. E. Kozhukhar, “Operatory Roty–Bakstera nenulevogo vesa na polnoi lineinoi algebre Li poryadka $2$ ”, Algebra i logika, 61:1 (2022), 93–97
M. Goncharov, “The description of Rota-Baxter operators of nonzero weight on complex general linear Lie algebra of order $2$ ”, Sib. elektron. matem. izv., 19:2 (2022), 870–879
M. E. Goncharov, D. E. Kozhukhar', “Rota–Baxter Operators of Nonzero Weight on a Complete Linear Lie Algebra of Order Two”, Algebra Logic, 61:1 (2022), 67
Fairon M., “Double Quasi-Poisson Brackets: Fusion and New Examples”, Algebr. Represent. Theory, 24:4 (2021), 911–958
D. V. Talalaev, “Tetrahedron equation: algebra, topology, and integrability”, Russian Math. Surveys, 76:4 (2021), 685–721
V. Gubarev, “An example of a simple double Lie algebra”, Sib. elektron. matem. izv., 18:2 (2021), 834–844
V. Gubarev, “Rota–Baxter operators on unital algebras”, Mosc. Math. J., 21:2 (2021), 325–364
Leray J., “Shifted Double Lie-Rinehart Algebras”, Theory Appl. Categ., 35 (2020), 594–621
Powell G., “On double Poisson structures on commutative algebras”, J. Geom. Phys., 110 (2016), 1–8
A. I. Zobnin, “Anti-Frobenius algebras and associative Yang–Baxter equation”, Matem. modelirovanie, 26:11 (2014), 51–56

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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