Classical R-matrix structure for the Calogero model

TL;DR

This paper presents a classical R-matrix framework for the Calogero model's Lax representation, establishing its integrability and related algebraic structures through a dynamical, non-antisymmetric, and non-invertible R-matrix.

Contribution

It introduces a novel classical R-matrix structure for the Calogero model's Lax representation, linking it to integrability and algebraic structures.

Findings

R-matrix is dynamical, non-antisymmetric, and non-invertible.

Establishes integrability for Type I, II, and III potentials.

Connects algebraic structures with Type V potential.

Abstract

A classical R-matrix structure is described for the Lax representation of the integrable n-particle chains of Calogero-Olshanetski-Perelo\-mov. This R-matrix is dynamical, non antisymmetric and non-invertible. It immediately triggers the integrability of the Type I, II and III potentials, and the algebraic structures associated with the Type V potential.