On a class of gl(n) ⊗ gl(n)-valued classical r-matrices and separation of variables

DOI10.1063/5.0041967zbMath1464.70010OpenAlexW3171954690MaRDI QIDQ5000224

T. V. Skrypnik

Publication date: 9 July 2021

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

Full work available at URL: https://doi.org/10.1063/5.0041967

Mathematics Subject Classification ID

Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)

Related Items

Anisotropic Z n-graded classical r-matrix, deformed A n Toda- and Gaudin-type models, and separation of variables, Separation of variables for the classical elliptic reflection equation algebra

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Integrable quantum spin chains, non-skew symmetric \(r\)-matrices and quasigraded Lie algebras
• Separation of variables in the classical integrable \(\mathrm{SL}(3)\) magnetic chain
• Darboux coordinates and Liouville-Arnold integration in loop algebras
• Separation of variables in the classical \(\mathrm{SL}(N)\) magnetic chain
• Separation of variables in anisotropic models and non-skew-symmetric elliptic \(r\)-matrix
• Orbit approach to separation of variables in \(\mathfrak{sl}(3)\)-related integrable systems
• Reductions in finite-dimensional integrable systems and special points of 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
• Infinite-dimensional Lie algebras, classical r-matrices, and Lax operators: Two approaches
• Quadratic algebras and integrable systems