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

1993/12/06 by E. Billey, Jean Avan, J. Avan +1 · 3 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Computer science #Construct (python library) #Euler's formula #Generalization #Geometry #Mathematical analysis #Mathematics #Matrix (chemical analysis) #Molecular spectroscopy and chirality #Nonlinear Waves and Solitons #Pure mathematics #Reduction (mathematics) #hep-th #nlin.SI #solv-int

paper · pdf · doi:10.1016/0375-9601(94)90930-x

7 pages

arxiv created 1993/12/06 · openalex publication_date 1994/03/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Exchange operator formalism for integrable systems of particles
• Explicit Solution to the N-Body Calogero Problem
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• Differential-difference operators associated to reflection groups

Cited by

• Liouville Integrability of a Class of Integrable Spin Calogero-Moser Systems and Exponents of Simple Lie Algebras
• On R -matrix valued Lax pairs for Calogero–Moser models
• The classical r-matrix for the relativistic Ruijsenaars-Schneider system
• Spin Calogero–Moser systems associated with simple Lie algebras