Shows Liouville integrability of the periodic Full Kostant-Toda lattice, suggesting new insights into simple Lie algebras.
We define the periodic Full Kostant-Toda 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 R -matrix.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, R -matrices, invariant functions and root systems.
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K. Ben Abdeljelil (2011) studied this question.
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