The R-matrix structure of the Euler-Calogero-Moser model

Abstract

We construct the $r$-matrix for the generalization of the Calogero-Moser system introduced by Gibbons and Hermsen. By reduction procedures we obtain the $r$-matrix for the $O(N)$ Euler-Calogero-Moser model and for the standard $A_N$ Calogero-Moser model.

7 pages

References in corpus (5)

• Exchange Operator Formalism for Integrable Systems of Particles
• Explicit Solution to the N-Body Calogero Problem
• Classical R-matrix structure for the Calogero model
• The Sine-Gordon Solitons as a N-Body Problem
• The Lie-Poisson Structure of Integrable Classical Non-Linear Sigma Models

Cited by in corpus (27)

• The Gervais-Neveu-Felder equation and the quantum Calogero-Moser systems
• Integrable spin Calogero-Moser systems
• Characteristic Classes of SL(N)-Bundles and Quantum Dynamical Elliptic R-Matrices
• Rational Top and its Classical R-matrix
• Spin Calogero models obtained from dynamical r-matrices and geodesic motion
• Elliptic Ruijsenaars-Schneider and Calogero-Moser hierarchies are governed by the same r-matrix
• Why are the rational and hyperbolic Ruijsenaars-Schneider hierarchies governed by the same R-operators as the Calogero-Moser ones?
• Spin Calogero-Moser systems associated with simple Lie algebras
• Classification of Isomonodromy Problems on Elliptic Curves
• Characteristic Classes and Integrable Systems. General Construction
• Generalized model of interacting integrable tops
• BPS Operators in N=4 SYM: Calogero Models and 2D Fermions
• On R-matrix valued Lax pairs for Calogero-Moser models
• The Classical $r$-Matrix for the Relativistic Ruijsenaars-Schneider System
• Observable algebra for the rational and trigonometric Euler Calogero Moser models
• Integrable discretizations of the spin Ruijsenaars-Schneider models
• GL(NM) quantum dynamical $R$-matrix based on solution of the associative Yang-Baxter equation
• Relativistic interacting integrable elliptic tops
• Non-ultralocal classical r-matrix structure for 1+1 field analogue of elliptic Calogero-Moser model
• Liouville integrability of a class of integrable spin Calogero-Moser systems and exponents of simple Lie algebras
• On the field analogue of elliptic spin Calogero-Moser model: Lax pair and equations of motion
• A Class of integrable Spin Calogero-Moser systems II: Exact Solvability
• Spin Calogero models and dynamical r-matrices
• Dirac structures and dynamical r-matrices
• Multi-pole extension for elliptic models of interacting integrable tops
• Classical dynamical r-matrices for Calogero-Moser systems and their generalizations
• Quantum Dynamical $\check{R}$- Matrix with Spectral Parameter from Fusion