Lie Algebroids and Classification Problems in Geometry

TL;DR

This paper introduces a method to associate classifying Lie algebroids to finite type G-structures, providing a unified framework for modeling geometries and their symmetry groups.

Contribution

It presents a novel approach linking G-structures with Lie algebroids and groupoids for classification and symmetry analysis in geometry.

Findings

Construction of classifying Lie algebroids for finite type G-structures

Lie groupoids model different geometries within the class

Encoding of symmetry groups through the groupoid structure

Abstract

We show how one can associate to a given class of finite type G-structures a classifying Lie algebroid. The corresponding Lie groupoid gives models for the different geometries that one can find in the class, and encodes also the different types of symmetry groups.