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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 12 scientific papers (total in 12 papers)

Classification of constant solutions of the associative Yang–Baxter equation on $\operatorname{Mat}_3$

V. V. Sokolov

Landau Institute for Theoretical Physics, Moscow, Russia
Full-text PDF (377 kB) Citations (12)
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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 $\operatorname{Mat}_3$. 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 $\operatorname{Mat}_3$”, TMF, 176:3 (2013), 385–392; Theoret. and Math. Phys., 176:3 (2013), 1156–1162
Citation in format AMSBIB
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    • This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:59
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