Geodesic
The Integrability of the Periodic Full Kostant-Toda Lattice on a Simple Lie Algebra
Journal of Lie theory, Tome 21 (2011) no. 4, pp. 929-96 Cet article a éte moissonné depuis la source Heldermann Verlag

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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.
Classification : 17B20,17B80,53D17
Mots-clés : Periodic Full Kostant-Toda lattice, integrable system, R-matrix, simple Lie algebra 
@article{JLT_2011_21_4_JLT_2011_21_4_a9,
     author = {K. Ben Abdeljelil },
     title = {The {Integrability} of the {Periodic} {Full} {Kostant-Toda} {Lattice} on a {Simple} {Lie} {Algebra}},
     journal = {Journal of Lie theory},
     pages = {929--96},
     year = {2011},
     volume = {21},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2011_21_4_JLT_2011_21_4_a9/}
}
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K. Ben Abdeljelil . The Integrability of the Periodic Full Kostant-Toda Lattice on a Simple Lie Algebra. Journal of Lie theory, Tome 21 (2011) no. 4, pp. 929-96. http://geodesic.mathdoc.fr/item/JLT_2011_21_4_JLT_2011_21_4_a9/