Reduction of a symplectic-like Lie algebroid with momentum map and its application to fiberwise linear Poisson structures

TL;DR

This paper extends the Marsden-Weinstein reduction to symplectic Lie algebroids, focusing on fiberwise linear Poisson structures, providing a new framework for reduction analogous to cotangent bundle reduction.

Contribution

It develops a reduction process for symplectic Lie algebroids with momentum maps, specifically applied to fiberwise linear Poisson structures, generalizing classical reduction methods.

Findings

Extended Marsden-Weinstein reduction to symplectic Lie algebroids.

Applied reduction to fiberwise linear Poisson structures.

Established a framework analogous to cotangent bundle reduction.

Abstract

This article addresses the problem of developing an extension of the Marsden- Weinstein reduction process to symplectic Lie algebroids, and in particular to the case of the symplectic cover of a fiberwise linear Poisson structure, whose reduction process is the analogue to cotangent bundle reduction in the context of Lie algebroids.