Symplectic reduction and a Darboux-Moser-Weinstein theorem for Lie algebroids

TL;DR

This paper extends fundamental symplectic reduction and embedding theorems to the setting of symplectic Lie algebroids, broadening the scope of classical symplectic geometry results.

Contribution

It introduces generalized versions of the Marsden-Weinstein and Darboux-Moser-Weinstein theorems for symplectic Lie algebroids, including a coisotropic embedding theorem.

Findings

Extended symplectic reduction to Lie algebroids

Established a Darboux-Moser-Weinstein theorem for Lie algebroids

Proved a coisotropic embedding theorem for symplectic Lie algebroids

Abstract

We extend the Marsden-Weinstein reduction theorem and the Darboux-Moser-Weinstein theorem to symplectic Lie algebroids. We also obtain a coisotropic embedding theorem for symplectic Lie algebroids.