Geodesic
Quantum current lie algebra as the universal algebraic structure of the symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics
Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 1, pp. 3-17 
N. N. Bogolyubov (Jr.); A. K. Prikarpatskii. Quantum current lie algebra as the universal algebraic structure of the symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics. Teoretičeskaâ i matematičeskaâ fizika, Tome 75 (1988) no. 1, pp. 3-17. http://geodesic.mathdoc.fr/item/TMF_1988_75_1_a0/
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     author = {N. N. Bogolyubov (Jr.) and A. K. Prikarpatskii},
     title = {Quantum current lie algebra as the universal algebraic structure of the symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {3--17},
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     volume = {75},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1988_75_1_a0/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

A new and extremely important property of the algebraic structure of symmetries of nonlinear infinite-dimensional integrable Hamiltonian dynamical systems is described. It is that their invariance groups are isomorphic to a unique universal Banach Lie group of currents $G=\mathcal I\odot\mathrm{diff}(T^n)$ on an $n$-dimensional torus $T^n$. Applications of this phenomenon to the problem of constructing general criteria of integrability of nonlinear dynamical systems of theoretical and mathematical physics are considered.

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