Separation of variables for quadratic algebras and skew-symmetric classical r-matrices

DOI10.1063/1.5100680zbMath1436.70005OpenAlexW2975232095MaRDI QIDQ5235529

B. A. Dubrovin, T. V. Skrypnik

Publication date: 11 October 2019

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

Full work available at URL: https://doi.org/10.1063/1.5100680

zbMATH Keywords

Sklyanin algebra

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) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06)

Related Items

New separation of variables for the classical \(XXX\) and \(XXZ\) Heisenberg spin chains, Separation of variables for the classical elliptic reflection equation algebra, Separation of variables for quadratic algebras: Algebras of Maillet and reflection-equation algebras

Cites Work

• Separation of variables in the classical integrable \(\mathrm{SL}(3)\) magnetic chain
• Separation of variables for the Ruijsenaars system
• Separation of variables in the classical \(\mathrm{SL}(N)\) magnetic chain
• Classical Yang–Baxter equations and quantum integrable systems
• Compatible Poisson brackets, quadratic Poisson algebras and classical r-matrices
• Classical functional Bethe ansatz for SL(N): Separation of variables for the magnetic chain
• Separation of variables for linear Lax algebras and classical r-matrices
• Solutions of the classical Yang-Baxter equation for simple Lie algebras
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