
Journal of Lie Theory 21 (2011), No. 4, 929960 Copyright Heldermann Verlag 2011 The Integrability of the Periodic Full KostantToda Lattice on a Simple Lie Algebra Khaoula Ben Abdeljelil Laboratoire de Mathématiques, Route de Chartres, B. P. 6759, 45067 Orléans, France khaoula@math.univpoitiers.fr We define the periodic Full KostantToda lattice on every simple Lie algebra, and show its Liouville integrability. More precisely we show that this lattice is given by a Hamiltonian vector field, associated to a Poisson bracket which results from an Rmatrix. We construct a large family of constants of motion which we use to prove the Liouville integrability of the system with the help of several results on simple Lie algebras, Rmatrices, invariant functions and root systems. Keywords: Periodic Full KostantToda lattice, integrable system, Rmatrix, simple Lie algebra. MSC: 17B20,17B80,53D17 [ Fulltextpdf (436 KB)] for subscribers only. 