Linear and multiplicative 2-forms

TL;DR

This paper explores the connection between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, offering a new perspective on their infinitesimal description and integration of twisted Dirac structures.

Contribution

It introduces a novel approach linking multiplicative and linear 2-forms, advancing the understanding of their infinitesimal and global properties.

Findings

Established a correspondence between multiplicative 2-forms and linear 2-forms

Provided a new method for integrating twisted Dirac manifolds

Enhanced the theoretical framework connecting Lie groupoids and Lie algebroids

Abstract

We study the relationship between multiplicative 2-forms on Lie groupoids and linear 2-forms on Lie algebroids, which leads to a new approach to the infinitesimal description of multiplicative 2-forms and to the integration of twisted Dirac manifolds.