On the Structure of Lie Pseudo-Groups

TL;DR

This paper compares two approaches to the structure theory of Lie pseudo-groups, highlighting the advantages of the authors' approach over Cartan's in both theory and practice.

Contribution

It introduces and advocates for a new approach to Lie pseudo-group structure theory, emphasizing its theoretical and practical benefits.

Findings

The authors' approach offers advantages over Cartan's method.

The paper clarifies the theoretical framework of Lie pseudo-groups.

Practical applications of the new approach are discussed.

Abstract

We compare and contrast two approaches to the structure theory for Lie pseudo-groups, the first due to Cartan, and the second due to the first two authors. We argue that the latter approach offers certain advantages from both a theoretical and practical standpoint.