Multiplicative forms at the infinitesimal level

TL;DR

This paper develops a comprehensive infinitesimal description of multiplicative differential forms on Lie groupoids using Lie algebroid data, unifying various results in Poisson geometry and related fields.

Contribution

It provides a new unified framework for understanding multiplicative forms and multivector fields on Lie groupoids and their Lie algebroid counterparts.

Findings

Unified description of multiplicative forms and multivectors

Connections established between Lie groupoid and Lie algebroid theories

Encompasses many existing integration results in Poisson geometry

Abstract

We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known integration results related to Poisson geometry. We also revisit multiplicative multivector fields and their infinitesimal counterparts, drawing a parallel between the two theories.