arXiv subjects

Khaoula Ben Abdeljelil

Publications and source records attributed to Khaoula Ben Abdeljelil.

2 recordsLinked to original sources

arXiv2011

The integrability of the periodic Full Kostant-Toda on a simple Lie algebra

We define the periodic Full Kostant-Toda 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 constant of motion which we use to prove the Liouville integrability of the system with the help of several results on simple Lie algebras, R-matrix, invariant functions and root systems.

math.AG↗

arXiv2011

The integrability of the 2-Toda lattice on a simple Lie algebra

We define the 2-Toda lattice on every simple Lie algebra g, and we show its Liouville integrability. We show that this lattice is given by a pair of Hamiltonian vector fields, associated with a Poisson bracket which results from an R-matrix of the underlying Lie algebra. We construct a big family of constants of motion which we use to prove the Liouville integrability of the system. We achieve the proof of their integrability by using several results on simple Lie algebras, R-matrices, invariant functions and root systems.

math.AG↗