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This article is cited in 58 scientific papers (total in 58 papers)
Compatible Poisson Brackets on Lie Algebras
A. V. Bolsinova, A. V. Borisovb a M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
b M. V. Lomonosov Moscow State University
Abstract:
We discuss the relationship between the representation of an integrable system as an $L$-$A$-pair with a spectral parameter and the existence of two compatible Hamiltonian representations of this system. We consider examples of compatible Poisson brackets on Lie algebras, as well as the corresponding integrable Hamiltonian systems and Lax representations.
Received: 01.10.2000
Citation:
A. V. Bolsinov, A. V. Borisov, “Compatible Poisson Brackets on Lie Algebras”, Mat. Zametki, 72:1 (2002), 11–34; Math. Notes, 72:1 (2002), 10–30
Linking options:
https://www.mathnet.ru/eng/mzm400https://doi.org/10.4213/mzm400 https://www.mathnet.ru/eng/mzm/v72/i1/p11
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