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TMF, 1988, Volume 75, Number 1, Pages 3–17 (Mi tmf4523)  

Quantum current lie algebra as the universal algebraic structure of the symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics

N. N. Bogolyubov (Jr.), A. K. Prikarpatskii


Abstract: 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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English version:
Theoretical and Mathematical Physics, 1988, 75:1, 329–339

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Document Type: Article
Received: 13.11.1986

Citation: 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”, TMF, 75:1 (1988), 3–17; Theoret. and Math. Phys., 75:1 (1988), 329–339

Citation in format AMSBIB
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\by N.~N.~Bogolyubov (Jr.), A.~K.~Prikarpatskii
\paper Quantum current lie algebra as the universal algebraic structure of the symmetries of completely integrable nonlinear dynamical systems of theoretical and mathematical physics
\jour TMF
\yr 1988
\vol 75
\issue 1
\pages 3--17
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=955663}
\zmath{https://zbmath.org/?q=an:0657.35120}
\transl
\jour Theoret. and Math. Phys.
\yr 1988
\vol 75
\issue 1
\pages 329--339
\crossref{https://doi.org/10.1007/BF01017166}
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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