Singular reduction of Dirac structures

TL;DR

This paper extends the regular reduction process of Dirac manifolds to cases where the Lie group action is nonfree, by establishing new properties of invariant vector fields and one-forms.

Contribution

It generalizes Dirac reduction to nonfree group actions, providing foundational results on invariant vector fields and forms.

Findings

Reduction method applicable to nonfree actions

New properties of G-invariant vector fields

Enhanced understanding of Dirac structure symmetry

Abstract

The regular reduction of a Dirac manifold acted upon freely and properly by a Lie group is generalized to a nonfree action. For this, several facts about $G$-invariant vector fields and one-forms are shown.