Completely Integrable Systems Connected with Lie Algebras期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

Completely Integrable Systems Connected with Lie Algebras

Authors:	Stanisław P Kasperczuk

Institution:	(1) Institute of Physics, Pedagogical University, Plac Słowiański 6, 65-069 Zielona Góra, Poland

Abstract:	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: $\mathcal{A} \to \Lambda \to C \to \tilde \Lambda \to \{ .,.\} _{\tilde \Lambda } \to (A,\vartriangle )$ , where A is a Lie algebra ${\text{(R}}^{\text{3}} ,.,.]),\Lambda$ is a Lie–Poisson structure on R ₃, C is a Casimir for $\Lambda ,\{ .,.\} _{\tilde \Lambda }$ 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 $\{ ,\} _{\tilde \Lambda }$ , 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. This revised version was published online in July 2006 with corrections to the Cover Date.

Keywords:	Lie algebra Poisson manifold Casimir function Poisson bialgebra integrable system
本文献已被 SpringerLink 等数据库收录！