Symmetries and reduction of multiplicative 2-forms

TL;DR

This paper explores the symmetries of multiplicative 2-forms on Lie groupoids and their applications to Lie group actions on Dirac manifolds, extending recent work on Poisson actions.

Contribution

It introduces a framework for analyzing symmetries of multiplicative 2-forms and applies it to Lie group actions on Dirac manifolds and presymplectic groupoids.

Findings

Characterization of symmetries of multiplicative 2-forms

Extension of symmetry analysis to Dirac and presymplectic structures

Connection to recent work on Poisson actions

Abstract

This paper is concerned with symmetries of closed multiplicative 2-forms on Lie groupoids and their infinitesimal counterparts. We use them to study Lie group actions on Dirac manifolds by Dirac diffeomorphisms and their lifts to presymplectic groupoids, building on recent work of Fernandes-Ortega-Ratiu \cite{FOR} on Poisson actions.