Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 1 (2005), 010, 12 pages      nlin.SI/0511039      http://dx.doi.org/10.3842/SIGMA.2005.010

A Gentle (without Chopping) Approach to the Full Kostant-Toda Lattice

Pantelis A. Damianou a and Franco Magri b
a) Department of Mathematics and Statistics, University of Cyprus, 1678, Nicosia, Cyprus
b) Department of Mathematics, University of Milano Bicocca, Via Corsi 58, I 20126 Milano, Italy

Received September 22, 2005, in final form October 24, 2005; Published online October 25, 2005

Abstract
In this paper we propose a new algorithm for obtaining the rational integrals of the full Kostant-Toda lattice. This new approach is based on a reduction of a bi-Hamiltonian system on gl(n, R). This system was obtained by reducing the space of maps from Zn to GL(n, R) endowed with a structure of a pair of Lie-algebroids.

Key words: full Kostant-Toda lattice; integrability; bi-Hamiltonian structure.

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