The Classifying Lie Algebroid of a Geometric Structure II: G-structures with connection

TL;DR

This paper introduces a classifying Lie algebroid for G-structures with connection, capturing their equivalence properties and linking to Cartan's realization problem, advancing geometric structure classification.

Contribution

It constructs a classifying Lie algebroid for G-structures with connection, detailing its properties, integration, and relation to Cartan's realization problem.

Findings

The classifying Lie algebroid encodes all equivalence information.

Properties of the G-structure Lie algebroid are characterized.

Connections to Cartan's realization problem are established.

Abstract

Given a G-structure with connection satisfying a regularity assumption we associate to it a classifying Lie algebroid. This algebroid contains all the information about the equivalence problem and is an example of a G-structure Lie algebroid. We discuss the properties of this algebroid, the G-structure groupoids integrating it and the relationship with Cartan's realization problem.