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Mat. Zametki, 2002, Volume 72, Issue 1, Pages 11–34 (Mi mz400)  

This article is cited in 41 scientific papers (total in 41 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.

DOI: https://doi.org/10.4213/mzm400

Full text: PDF file (321 kB)
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English version:
Mathematical Notes, 2002, 72:1, 10–30

Bibliographic databases:

UDC: 517.9
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

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. I. Z. Golubchik, V. V. Sokolov, “Compatible Lie Brackets and Integrable Equations of the Principal Chiral Model Type”, Funct. Anal. Appl., 36:3 (2002), 172–181  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
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    4. Bolsinov A., “Integrable Geodesic Flows on Riemannian Manifolds: Construction and Obstructions”, Proceedings of the Workshop on Contemporary Geometry and Related Topics, eds. Bokan N., Djoric M., Fomenko A., Rakic Z., Wess J., World Scientific Publ Co Pte Ltd, 2004, 57–103  crossref  mathscinet  zmath  isi
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    6. L. G. Rybnikov, “The Argument Shift Method and the Gaudin Model”, Funct. Anal. Appl., 40:3 (2006), 188–199  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
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    12. A. V. Tsiganov, “Compatible Lie–Poisson brackets on the Lie algebras $e(3)$ and $so(4)$”, Theoret. and Math. Phys., 151:1 (2007), 459–473  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
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    19. Campoamor-Stursberg R., Musso F., “Two-Body Homogeneous Rational Gaudin Models and the Missing Label Problem”, J. Phys. A-Math. Theor., 46:33 (2013), 335201  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
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