A classical integrable Hamiltonian system is defined by an A belian 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 all example.
Ballesteros, A., Musso, F., Ragnisco, O. (2003). Maximally superintegrable Gaudin magnet: A unified approach RID A-7283-2010. THEORETICAL AND MATHEMATICAL PHYSICS, 137(3), 1645-1651 [10.1023/B:TAMP.0000007913.22639.d3].