Classical lifting processes and multiplicative vector fields

TL;DR

This paper generalizes the calculus of multiplicative vector fields and forms from Lie groups to Lie groupoids, providing new insights into Lie bialgebroid structures related to Poisson groupoids.

Contribution

It extends the calculus to Lie groupoids and offers a novel description of Lie bialgebroid structures associated with Poisson groupoids.

Findings

Extended calculus from Lie groups to Lie groupoids.

Unified description of classical lifting processes.

New characterization of Lie bialgebroid structures.

Abstract

We extend the calculus of multiplicative vector fields and differential forms and their intrinsic derivatives from Lie groups to Lie groupoids; this generalization turns out to include also the classical process of complete lifting from arbitrary manifolds to tangent and cotangent bundles. Using this calculus we give a new description of the Lie bialgebroid structure associated with a Poisson groupoid.