Astronomy and Astrophysics – Astronomy
Scientific paper
May 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000cemda..76..215k&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, v. 76, Issue 4, p. 215-227 (2000).
Astronomy and Astrophysics
Astronomy
1
Lie Algebra, Poisson Manifold, Casimir Function, Poisson Bialgebra, Integrable System, Lie Algebra, Poisson Manifold, Casimir Function, Poisson Bialgebra, Integrable System
Scientific paper
In a recent paper Ballersteros and Ragnisco (1998) have proposed a new method of constructing integrable Hamiltonian systems. A new class of integrable systems may be devised using the following sequence: A to Λ to C to tilde Λ to { .,.} _{tilde Λ } to (A,\vartriangle ), where A is a Lie algebra (R^{3} ,[.,.]),Λ is a Lie Poisson structure on R 3, C is a Casimir for Λ ,{ .,.} _{tilde Λ } is a reduced Poisson bracket and (A, ▵) is a bialgebra. We study the relation between a Lie-Poisson stucture Λ and a reduced Poisson bracket ,_{tilde Λ } , which is a key element in using the Lie algebra A to constructing this sequence. New examples of Lie algebras and their related integrable Hamiltonian systems are given.
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