Automorphisms of \(\text{sl}(2)\) and classical integrable systems

DOI10.1016/S0375-9601(98)00934-7zbMath0985.37069MaRDI QIDQ1967080

Andreĭ Vladimirovich Tsyganov

Publication date: 8 March 2000

Published in: Physics Letters. A (Search for Journal in Brave)

zbMATH Keywords

universal enveloping algebraloop algebraLax pairsinfinite-dimensional representationsouter automorphisms\(r\)-matrix algebras

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (1)

The Maupertuis Principle and Canonical Transformations of the Extended Phase Space

Cites Work

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• A new integrable case of the motion of the 4-dimensional rigid body
• Dynamical \(r\)-matrices for integrable maps
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• Automorphisms of sl(2) and dynamical r-matrices
• Integrable maps for the Garnier and for the Neumann system
• Dynamical boundary conditions for integrable lattices
• On different integrable systems sharing the same nondynamical r-matrix
• Integrability, Stäckel spaces, and rational potentials
• Linear r-matrix algebra for classical separable systems

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