Observable algebra for the rational and trigonometric Euler Calogero Moser models

TL;DR

This paper constructs polynomial Poisson algebras for classical Euler-Calogero-Moser models, revealing their structure and limits, including connections to -infinity type algebras and current algebras.

Contribution

It introduces a new algebraic framework for ECM models, extending previous conserved quantities and symmetries to polynomial Poisson algebras and their large N limits.

Findings

Polynomial Poisson algebras for ECM models constructed

Identification of -infinity type algebras in the large N limit

Connection between conserved Hamiltonians, symmetries, and algebraic structures

Abstract

We construct polynomial Poisson algebras of observables for the classical Euler-Calogero-Moser (ECM) models. The conserved Hamiltonians and symmetry algebras derived in a previous work are subsets of these algebras. We define their linear, $N \rightarrow \infty$ limits, realizing $\w_{\infty}$ type algebras coupled to current algebras.