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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
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
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
Linking options:
https://www.mathnet.ru/eng/tmf2031https://doi.org/10.4213/tmf2031 https://www.mathnet.ru/eng/tmf/v146/i2/p195
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Abstract page: | 686 | Full-text PDF : | 289 | References: | 98 | First page: | 1 |
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