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Mathematical Notes

, Volume 72, Issue 1–2, pp 10–30 | Cite as

Compatible Poisson Brackets on Lie Algebras

  • A. V. Bolsinov
  • A. V. Borisov
Article

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.

compatible Poisson brackets compatible Hamiltonian representation Lax representation integrable Hamiltonian system bi-Hamiltonian vector field Lie algebra 

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Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • A. V. Bolsinov
    • 1
  • A. V. Borisov
    • 1
  1. 1.M. V. Lomonosov Moscow State UniversityRussia

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