DEFORMATIONS OF LOOP ALGEBRAS AND CLASSICAL INTEGRABLE SYSTEMS: FINITE-DIMENSIONAL HAMILTONIAN SYSTEMS

DOI10.1142/S0129055X04002187zbMath1106.37038OpenAlexW2073077194MaRDI QIDQ4650678

T. V. Skrypnik

Publication date: 18 February 2005

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0129055x04002187

zbMATH Keywords

finite-dimensional Hamiltonian systemquasi-graded Lie algebradeformation of loop algebra

Mathematics Subject Classification ID

Infinite-dimensional Lie (super)algebras (17B65) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Momentum maps; symplectic reduction (53D20) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

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Decompositions of quasigraded Lie algebras, non-skew-symmetric classical \(r\)-matrices and generalized Gaudin models, Special quasigraded Lie algebras and integrable Hamiltonian systems, Quasi-periodic functions on the torus and sl(n)-elliptic Lie algebra

Cites Work

• Lie algebras and equations of Korteweg-de Vries type
• The solution to a generalized Toda lattice and representation theory
• Kowalewski's asymptotic method, Kac-Moody Lie algebras and regularization
• Generalized Drinfel'd-Sokolov hierarchies
• Reduction of Hamiltonian systems, affine Lie algebras and Lax equations
• Generalized Drinfeld-Sokolov reductions and KdV type hierarchies
• Compatible Lie brackets and integrable equations of the principal chiral model type
• Quasigraded deformations of loop algebras and classical integrable systems.
• Quasigraded Lie algebras on hyperelliptic curves and classical integrable systems