Dynamical systems on quantum tori Lie algebras

DOI10.1007/BF02096721zbMath0791.17024MaRDI QIDQ1308475

Jens Hoppe, Mikhail A. Olshanetsky, Stefan J. Theisen

Publication date: 21 July 1994

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

zbMATH Keywords

Toda chainintegrable dynamical systemsquantum tori Lie algebrastrigonometrical Lie 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 (super)algebras to physics, etc. (17B81) Infinite-dimensional Lie (super)algebras (17B65) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items

Between \(\widehat {\mathfrak {gl}} (\infty)\) and \(\widehat {\mathfrak {sl}}_ N\) affine algebras. I: Geometrical actions, Trigonometric Lie algebras, affine Kac-Moody Lie algebras, and equivariant quasi modules for vertex algebras, Vertex operator representation of some quantum tori Lie algebras, Intertwining operator and integrable hierarchies from topological strings, Quantum W1+∞ subalgebras of BCD type and symmetric polynomials, Generalized \(W_{\infty}\) higher-spin algebras and symbolic calculus on flag manifolds

Cites Work

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• Continuum analogues of contragredient Lie algebras. (Lie algebras with a Cartan operator and nonlinear dynamical systems)
• Solitons and infinite dimensional Lie algebras
• Lie algebras and equations of Korteweg-de Vries type
• A new integrable case of the motion of the 4-dimensional rigid body
• Nonlocal integrable partners to generalized MKdV and two-dimensional Toda lattice equation in the formalism of a dressing method with quantized spectral parameter
• Vertex operator representation of some quantum tori Lie algebras
• Theory of nonlinear lattices.
• Local area-preserving algebras for two-dimensional surfaces
• DIFFEOMORPHISM GROUPS, QUANTIZATION, AND SU(∞)
• Infinite-dimensional algebras and a trigonometric basis for the classical Lie algebras
• POSSIBLE IMPLICATIONS OF INTEGRABLE SYSTEMS FOR STRING THEORY