An extension of the Marsden-Ratiu reduction for Poisson manifolds

TL;DR

This paper generalizes the Marsden-Ratiu reduction method for Poisson manifolds, allowing for more flexible reductions that depend on distributions, with applications and algebraic interpretations explored.

Contribution

It introduces a broader reduction framework for Poisson manifolds that overcomes previous limitations and incorporates Dirac structures.

Findings

Reduced Poisson structures depend effectively on distributions.

The new method applies to various examples and contexts.

Algebraic and Dirac structure interpretations are provided.

Abstract

We propose a generalization of the reduction of Poisson manifolds by distributions introduced by Marsden and Ratiu. Our proposal overcomes some of the restrictions of the original procedure, and makes the reduced Poisson structure effectively dependent on the distribution. Different applications are discussed, as well as the algebraic interpretation of the procedure and its formulation in terms of Dirac structures.