Integrable quantum systems and classical Lie algebras
type: Item
instance of: scholarly article
title: Integrable quantum systems and classical Lie algebras
zbMATH Open document ID: 0629.58036
DOI: 10.1007/BF01221256
published in: Communications in Mathematical Physics
publication date: 1987-01-01T00:00:00Z
review text: We obtain six new infinite series of trigonometric solutions to triangle equations (quantum R-matrices) associated with the nonexceptional simple Lie algebras: \(s\ell (N)\), sp(N), o(N). The R-matrices are given in two equivalent representations: in an additive one (as a sum of poles with matrix coefficients) and in a multiplicative one (as a ratio of entire matrix functions). These R-matrices provide an exact integrability of anisotropic generalizations of \(s\ell (N)\), sp(N), o(N) invariant one- dimensional lattice magnetics and two-dimensional periodic Toda lattices associated with the above algebras.
Mathematics Subject Classification ID: 58Z05
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 35Q99
zbMATH DE Number: 4024366
zbMATH Keywords: trigonometric solutions to triangle equations
zbMATH Keywords: one-dimensional lattice magnetics
zbMATH Keywords: two-dimensional periodic Toda lattices
author: Vladimir V. Bazhanov
MaRDI profile type: Publication
cites work: Partition function of the eight-vertex lattice model
cites work: Q3324796
cites work: \(\mathrm{O}(N)\) invariant quantum field theoretical models: exact solution
cites work: Q3687118
cites work: Q3915370
cites work: Q3882854
cites work: Q3901715
cites work: Dynamical symmetry of integrable quantum systems
cites work: Solutions of the Yang-Baxter equation
cites work: The complex exponent of a singularity does not change along strata mu=const
cites work: Q3346994
cites work: Solutions of the classical Yang-Baxter equation for simple superalgebras
cites work: Q3793397
cites work: Quantum R matrix for the generalized Toda system
cites work: Quantum difference nonlinear Schrödinger equation
cites work: Q3957669
cites work: Two-dimensional generalized Toda lattice
cites work: The Riemannian geometry of the configuration space of gauge theories
full work available at URL: https://doi.org/10.1007/bf01221256
OpenAlex ID: W2019813441
description: scientific article; zbMATH DE number 4024366