The semi-direct product of Poisson $G$-spaces

TL;DR

This paper introduces the semi-direct product of Poisson G-spaces and applies it to analyze examples in spin-extensions of Ruijsenaars models, providing new insights into their structure.

Contribution

It develops the concept of semi-direct product for Poisson G-spaces and demonstrates its application to specific models in mathematical physics.

Findings

Clarifies the structure of spin-extensions of Ruijsenaars models

Provides a new framework for combining Poisson G-spaces

Enhances understanding of symmetries in integrable systems

Abstract

The notion of semi-direct product of Poisson $G$-spaces is applied to illuminate examples arising in spin-extensions of Ruijsenaars models.