Geodesic
Maximally Superintegrable Gaudin Magnet: A Unified Approach
Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 3, pp. 336-343

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A classical integrable Hamiltonian system is defined by an Abelian subalgebra (of suitable dimension) of a Poisson algebra, while a quantum integrable Hamiltonian system is defined by an Abelian subalgebra (of suitable dimension) of a Jordan–Lie algebra of Hermitian operators. We propose a method for obtaining “large” Abelian subalgebras inside the tensor product of free tensor algebras, and we show that there exist canonical morphisms from these algebras to Poisson algebras and Jordan–Lie algebras of operators. We can thus prove the integrability of some particular Hamiltonian systems simultaneously at both the classical and the quantum level. We propose a particular case of the rational Gaudin magnet as an example.
Keywords: superintegrability, Gaudin magnet
Mots-clés : coalgebras. 
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Á. Ballesteros; F. Musso; O. Ragnisco. Maximally Superintegrable Gaudin Magnet: A Unified Approach. Teoretičeskaâ i matematičeskaâ fizika, Tome 137 (2003) no. 3, pp. 336-343. http://geodesic.mathdoc.fr/item/TMF_2003_137_3_a2/