The Classifying Lie Algebroid of a Geometric Structure I: Classes of Coframes

TL;DR

This paper introduces a classifying Lie algebroid to systematically analyze symmetries, invariants, and moduli spaces of coframes, providing a comprehensive solution to Cartan's realization problem for both local and global cases.

Contribution

It develops a novel classifying Lie algebroid framework that unifies the treatment of Cartan's realization problem for geometric structures.

Findings

Complete description of solutions to Cartan's realization problem

Unified approach for local and global geometric structures

New insights into symmetries and invariants of coframes

Abstract

We present a systematic study of symmetries, invariants and moduli spaces of classes of coframes. We introduce a classifying Lie algebroid to give a complete description of the solution to Cartan's realization problem that applies to both the local and the global versions of this problem.