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

Journal Article · Sat Oct 01 00:00:00 EDT 1988 · Theor. Math. Phys.; (United States)

DOI:https://doi.org/10.1007/BF01017166· OSTI ID:5705952

Bogolyubov, Jr, N N; Prikarpatskii, A K

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 = l /circled dot/Diff (T/sup n/) on an n-dimensional torus T/sup 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.

• OSTI ID: 5705952
• Journal Information: Theor. Math. Phys.; (United States), Vol. 75:1; Other Information: Translated from Teor. Mat. Fiz.; 75: No. 1, 3-17(Apr 1988)
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
LIE GROUPS
CURRENT ALGEBRA
ALGEBRAIC CURRENTS
BANACH SPACE
COMMUTATION RELATIONS
HAMILTONIANS
HILBERT SPACE
INVARIANCE PRINCIPLES
IRREDUCIBLE REPRESENTATIONS
KORTEWEG-DE VRIES EQUATION
NONLINEAR PROBLEMS
PARTICLE MODELS
QUANTUM MECHANICS
TORI
UNITARY SYMMETRY
CURRENTS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICAL SPACE
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM OPERATORS
SPACE
SYMMETRY
SYMMETRY GROUPS
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