Differential invariants of a Lie group action: syzygies on a generating set

TL;DR

This paper develops a comprehensive method for deriving all relations among differential invariants of a Lie group action using Cartan's moving frame reinterpretation, aiding the analysis of invariant algebras.

Contribution

It introduces a complete set of syzygies on differential invariants based on a reinterpretation of Cartan's moving frame, providing new constructive tools.

Findings

Complete syzygies on differential invariants established

Enhanced understanding of algebraic structure of invariants

Constructive methods for exploring invariant algebras

Abstract

Given a group action, known by its infinitesimal generators, we exhibit a complete set of syzygies on a generating set of differential invariants. For that we elaborate on the reinterpretation of Cartan's moving frame by Fels and Olver (1999). This provides constructive tools for exploring algebras of differential invariants.