Journal of Lie Theory

no. 4
The Integrability of the Periodic Full Kostant-Toda Lattice on a Simple Lie Algebra
Journal of Lie Theory, Volume 21 (2011) no. 4, pp. 929-960
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.
DOI: 10.5802/jolt.656
Classification: 17B20,17B80,53D17
Keywords: Periodic Full Kostant-Toda lattice, integrable system, R-matrix, simple Lie algebra 
@article{JOLT_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--960},
     year = {2011},
     volume = {21},
     number = {4},
     doi = {10.5802/jolt.656},
     zbl = {1264.17018},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.656/}
}
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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, Volume 21 (2011) no. 4, pp. 929-960. doi: 10.5802/jolt.656

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