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Teoreticheskaya i Matematicheskaya Fizika, 2006, Volume 146, Number 2, Pages 195–207
DOI: https://doi.org/10.4213/tmf2031 (Mi tmf2031) 		 
This article is cited in 22 scientific papers (total in 22 papers)

Compatible Lie Brackets and the Yang–Baxter Equation

I. Z. Golubchika, V. V. Sokolovb

a Bashkir State Pedagogical University
b L. D. Landau Institute for Theoretical Physics, Russian Academy of Sciences
Full-text PDF (188 kB) Citations (22)
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DOI: https://doi.org/10.4213/tmf2031
Abstract: We show that any pair of compatible Lie brackets with a common invariant form produces a nonconstant solution of the classical Yang–Baxter equation. We describe the corresponding Poisson brackets, Manin triples, and Lie bialgebras. It turns out that all bialgebras associated with the solutions found by Belavin and Drinfeld are isomorphic to some bialgebras generated by our solutions. For any compatible pair, we construct a double with a common invariant form and find the corresponding solution of the quantum Yang–Baxter equation for this double.
Keywords: Yang–Baxter equation, Lie bialgebra, Manin triple.
Received: 18.03.2005
English version:
Theoretical and Mathematical Physics, 2006, Volume 146, Issue 2, Pages 159–169
DOI: https://doi.org/10.1007/s11232-006-0016-6
Bibliographic databases:
Language: Russian
Citation: I. Z. Golubchik, V. V. Sokolov, “Compatible Lie Brackets and the Yang–Baxter Equation”, TMF, 146:2 (2006), 195–207; Theoret. and Math. Phys., 146:2 (2006), 159–169
Citation in format AMSBIB
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    • This publication is cited in the following 22 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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