Separation of variables, Lax-integrable systems and \(gl(2) \otimes gl(2)\)-valued classical \(r\)-matrices

DOI10.1016/j.geomphys.2020.103733zbMath1450.37054OpenAlexW3024060134MaRDI QIDQ778978

T. V. Skrypnik

Publication date: 21 July 2020

Published in: Journal of Geometry and Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.geomphys.2020.103733

zbMATH Keywords

separation of variablesclassical \(r\)-matricesGaudin-type models

Mathematics Subject Classification ID

Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Exactly solvable models; Bethe ansatz (82B23) Applications of Lie algebras and superalgebras to integrable systems (17B80) Relations of finite-dimensional Hamiltonian and Lagrangian systems with Lie algebras and other algebraic structures (37J37)

Related Items (5)

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 ⋮ Elliptic Gaudin-type model in an external magnetic field and modified algebraic Bethe ansatz ⋮ Separation of variables, quasi-trigonometric \(r\)-matrices and generalized Gaudin models ⋮ Anisotropic BCS-Richardson model and algebraic Bethe ansatz

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Separation of variables in the Gaudin model
• Spin chains in magnetic field, non-skew-symmetric classical r-matrices and BCS-type integrable systems
• A Lie algebraic generalization of the Mumford system, its symmetries and its multi-Hamiltonian structure
• Darboux coordinates and Liouville-Arnold integration in loop algebras
• Integrable systems and symmetric products of curves
• Quasigraded deformations of loop algebras and classical integrable systems.
• Dual moment maps into loop algebras
• Canonically Conjugate Variables for the Korteweg-de Vries Equation and the Toda Lattice with Periodic Boundary Conditions
• Reductions in finite-dimensional integrable systems and special points of classical r-matrices
• Non-skew-symmetric classical r-matrices, algebraic Bethe ansatz, and Bardeen–Cooper–Schrieffer–type integrable systems
• “Many-poled” r-matrix Lie algebras, Lax operators, and integrable systems
• Non-skew-symmetric classicalr-matrices and integrable cases of the reduced BCS model
• New non-skew symmetric classicalr-matrices and ‘twisted’ quasigraded Lie algebras
• Generalized quantum Gaudin spin chains, involutive automorphisms and “twisted” classical r-matrices
• Investigation of Equations of Korteweg-De Vries Type by the Method of Recurrence Relations
• Separation of variables for linear Lax algebras and classical r-matrices
• Infinite-dimensional Lie algebras, classical r-matrices, and Lax operators: Two approaches
• Generalized Gaudin systems in a magnetic field and non-skew-symmetricr-matrices
• Spectroscopy of discrete energy levels in ultrasmall metallic grains

This page was built for publication: Separation of variables, Lax-integrable systems and \(gl(2) \otimes gl(2)\)-valued classical \(r\)-matrices