Compatible Poisson brackets on Lie algebras

被引：44

作者：

Bolsinov, AV ^{[1
]}

Borisov, AV ^{[1
]}

机构：

[1] Moscow MV Lomonosov State Univ, Moscow 119899, Russia

来源：

MATHEMATICAL NOTES | 2002年 / 72卷 / 1-2期

基金：

俄罗斯基础研究基金会;

关键词：

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

D O I：

10.1023/A:1019856702638

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：10 / 30

页数：21

共 31 条

[1] GEODESIC-FLOW ON SO(4) AND THE INTERSECTION OF QUADRICS
ADLER, M
VANMOERBEKE, P
[J]. PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA-PHYSICAL SCIENCES, 1984, 81 (14): : 4613 - 4616
[2] BOBENKO AI, 1986, FUNCT ANAL PRIL, V20, P64
[3] BOGOYAVLENSKII OI, 1984, IZV AN SSSR M, V48, P883
[4] Theory of tensor invariants of integrable Hamiltonian systems .1. Incompatible Poisson structures
Bogoyavlenskij, OI
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1996, 180 (03) : 529 - 586
[5] Extended integrability and bi-Hamiltonian systems
Bogoyavlenskij, OI
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1998, 196 (01) : 19 - 51
[6] Theory of tensor invariants of integrable Hamiltonian systems .2. Theorem on symmetries and its applications
Bogoyavlenskij, OI
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1997, 184 (02) : 301 - 365
[7] BOLSINOV AV, VESTNIK MOSKOV U SER, P53
[8] BOLSINOV AV, 1991, P SEM VECT TENS AN, P8
[9] BOLSINOV AV, 1991, IZV AKAD NAUK SSSR S, V5, P68
[10] BORISOV AV, 1999, POISSON STRUCTURES L

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