Compatible Lie brackets related to elliptic curve

DOI10.1063/1.2158434zbMath1111.17008arXivmath/0506503OpenAlexW3100901507MaRDI QIDQ3438754

Vladimir Sokolov, Alexander Odesskii

Publication date: 16 May 2007

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

Full work available at URL: https://arxiv.org/abs/math/0506503

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (9)

Noncommutative Poisson bialgebras ⋮ The category and operad of matching dialgebras ⋮ Compatible \(L_\infty \)-algebras ⋮ Cohomology and deformations of compatible Lie triple systems ⋮ Maurer-Cartan characterizations and cohomologies of compatible Lie algebras ⋮ (Co)homology of compatible associative algebras ⋮ Totally compatible associative and Lie dialgebras, tridendriform algebras and PostLie algebras ⋮ Bi-Hamiltonian structures and singularities of integrable systems ⋮ Pairs of compatible associative algebras, classical Yang-Baxter equation and quiver representations

Cites Work

• Factorization of the loop algebra and integrable toplike systems
• Separation of variables in the elliptic Gaudin model.
• Compatible Poisson brackets on Lie algebras
• Compatible Lie brackets and integrable equations of the principal chiral model type
• Bihamiltonian structures and quadratic algebras in hydrodynamics and on non-commutative torus
• Vector Bundles Over an Elliptic Curve
• A simple model of the integrable Hamiltonian equation
• Elliptic algebras
• Webs, Lenard schemes, and the local geometry of bi-Hamiltonian Toda and Lax structures

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