New non-skew symmetric classicalr-matrices and ‘twisted’ quasigraded Lie algebras

DOI10.1088/1751-8113/40/7/012zbMath1108.37047OpenAlexW2070816740MaRDI QIDQ3425232

T. V. Skrypnik

Publication date: 7 March 2007

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

Full work available at URL: https://doi.org/10.1088/1751-8113/40/7/012

zbMATH Keywords

Yang-Baxter equationintegrable Hamiltonian systemsquantum integrable systemsKostant-Adler schemequasigraded deformations

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Quantum groups and related algebraic methods applied to problems in quantum theory (81R50) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Groups and algebras in quantum theory and relations with integrable systems (81R12) Graded Lie (super)algebras (17B70) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures (37K30)

Related Items (13)

On the general solution of the permuted classical Yang–Baxter equation and quasigraded Lie algebras ⋮ Anisotropic Z n-graded classical r-matrix, deformed A n Toda- and Gaudin-type models, and separation of variables ⋮ Elliptic BCS-Richardson model and the modified algebraic Bethe ansatz ⋮ Decompositions of quasigraded Lie algebras, non-skew-symmetric classical \(r\)-matrices and generalized Gaudin models ⋮ Reductions in finite-dimensional integrable systems and special points of classical r-matrices ⋮ Classical $r$-matrices, ``elliptic BCS and Gaudin-type Hamiltonians and spectral problem ⋮ Elliptic Gaudin-type model in an external magnetic field and modified algebraic Bethe ansatz ⋮ Elliptic three-boson system, ``two-level three-mode JCD-type models and non-skew-symmetric classical r-matrices ⋮ Separation of variables for quadratic algebras: Algebras of Maillet and reflection-equation algebras ⋮ Twisted rational \(r\)-matrices and algebraic Bethe ansatz: application to generalized Gaudin and Richardson models ⋮ Anisotropic BCS-Richardson model and algebraic Bethe ansatz ⋮ Separation of variables, Lax-integrable systems and \(gl(2) \otimes gl(2)\)-valued classical \(r\)-matrices ⋮ Isomonodromic deformations, generalized Knizhnik–Zamolodchikov equations and non-skew-symmetric classical r-matrices

This page was built for publication: New non-skew symmetric classicalr-matrices and ‘twisted’ quasigraded Lie algebras