Involutive moving frames II; The Lie-Tresse theorem

2020/11/10 by Arnaldsson, Örn
#22F05 #53A55 #58A15 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.05101

Abstract

This paper continues the project, begun in \citeIMF, of harmonizing Cartan's classical equivalence method and the modern equivariant moving frame in a framework dubbed involutive moving frames. As an attestation of the fruitfulness of our framework, we obtain a new, constructive and intuitive proof of the Lie-Tresse theorem (Fundamental basis theorem) and a first general upper bound on the minimal number of generating differential invariants for Lie pseudo-groups. Further, we demonstrate the computational advantages of this framework by studying the equivalence problem for first order PDE in two independent variables and one dependent variable under point transformations.

Related

• Involutive moving frames
• Inductive Approach to Cartan's Moving Frame Method with Applications to Classical Invariant Theory
• Introducing the Classical Method of Moving Frames
• The equivariant moving frame method of third order differential equations
• Invariants: Computation and Applications