Liouville integrability of a class of integrable spin Calogero-Moser systems and exponents of simple Lie algebras

TL;DR

This paper proves the Liouville integrability of a class of spin Calogero-Moser systems linked to simple Lie algebras using a unified approach, expanding understanding of their integrable structure.

Contribution

It establishes the Liouville integrability of these systems through a uniform method, building on prior classification of classical dynamical r-matrices.

Findings

Liouville integrability of the systems is proven

A uniform method for establishing integrability is developed

Enhances understanding of spin Calogero-Moser systems

Abstract

In previous work, we introduced a class of integrable spin Calogero-Moser systems associated with the classical dynamical r-matrices with spectral parameter, as classified by Etingof and Varchenko for simple Lie algebras. Here the main purpose is to establish the Liouville integrability of these systems by a uniform method.