Quadratic algebras related to elliptic curves
DOI10.1007/s11232-008-0081-0zbMath1160.37023arXiv0710.1072OpenAlexW2593391005MaRDI QIDQ954337
Publication date: 10 November 2008
Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/0710.1072
Quantum groups (quantized enveloping algebras) and related deformations (17B37) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30) Poisson algebras (17B63) Quadratic algebras (but not quadratic Jordan algebras) (17A45)
Related Items (13)
Cites Work
- Sklyanin elliptic algebras
- Painlevé VI, rigid tops and reflection equation
- Some algebraic structures connected with the Yang-Baxter equation
- Discrete groups and the integrability of quantum systems
- Gaudin model, KZ equation and an isomonodromic problem on the torus
- Bihamiltonian structures and quadratic algebras in hydrodynamics and on non-commutative torus
- Elliptic Schlesinger system and Painlevé VI
- Classicalr-matrices and the Feigin–Odesskii algebra via Hamiltonian and Poisson reductions
- Solutions of the classical Yang-Baxter equation for simple Lie algebras
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