Projections of Jordan bi-Poisson structures that are Kronecker, diagonal actions, and the classical Gaudin systems

JOURNAL OF GEOMETRY AND PHYSICS

卷:47

Article

Panasyuk, A

关键词: bihamiltonian;    bi-Poisson structures;    Poisson reduction;    completely integrable systems;   

DOI  :  10.1016/S0393-0440(02)00228-0

来源: Elsevier

【 摘 要 】

We propose a method of constructing completely integrable systems based on reduction of bi-hamiltonian structures. More precisely, we give an easily checkable necessary and sufficient conditions for the micro-kroneckerity of the reduction (per-formed with respect to a special type action of a Lie group) of micro-Jordan bihamiltonian structures whose Nijenhuis tensor has constant eigen-values. The method is applied to the diagonal action of a Lie group G on a direct product of N coadjoint orbits O = O-1 x (...) x O-N subset of g* x (...) x g* endowed with a bihamiltonian structure whose first generator is the standard symplectic form on O. As a result we get the so-called classical Gaudin system on O. The method works for a wide class of Lie algebras including the semisimple ones and for a large class of orbits including the generic ones and the semisimple ones. (C) 2002 Elsevier Science B.V. All rights reserved.

【 授权许可】

Free