Multi-Hamiltonian structures for r-matrix systems

Simple item page
dc.creatorHarnad, J.
dc.creatorHurtubise, J. C.
dc.date2002-11-29
dc.date.accessioned2026-07-07T12:32:39Z
dc.date.available2026-07-07T12:32:39Z
dc.descriptionFor the rational, elliptic and trigonometric r-matrices, we exhibit the links between three "levels" of Poisson spaces: (a) Some finite-dimensional spaces of matrix-valued holomorphic functions on the complex line; (b) Spaces of spectral curves and sheaves supported on them; (c) Symmetric products of a surface. We have, at each level, a linear space of compatible Poisson structures, and the maps relating the levels are Poisson. This leads in a natural way to Nijenhuis coordinates for these spaces. At level (b), there are Hamiltonian systems on these spaces which are integrable for each Poisson structure in the family, and which are such that the Lagrangian leaves are the intersections of the symplective leaves over the Poisson structures in the family. Specific examples include many of the well-known integrable systems.
dc.description26 pages, Plain Tex
dc.identifierhttps://arxiv.org/abs/math-ph/0211076
dc.identifierhttp://arxiv.org/abs/math-ph/0211076
dc.identifierJ.Math.Phys.49:062903,2008
dc.identifierdoi:10.1063/1.2937896
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/216853
dc.subjectMathematical Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectSymplectic Geometry
dc.subjectExactly Solvable and Integrable Systems
dc.titleMulti-Hamiltonian structures for r-matrix systems
dc.typetext

Files

Collections

arXiv