On the Structure of Lie Pseudo-Groups

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.

Keywords

• Lie pseudo-group
• infinitesimal generator
• jet
• contact form
• Maurer-Cartan form
• structure equations
• essential invariant