Lie Transformation Groups -- An Introduction to Symmetry Group Analysis of Differential Equations

TL;DR

This paper provides an introductory lecture note on symmetry group analysis of differential equations, covering local transformation groups and their applications, based on Olver's foundational work, suitable for readers with basic differential geometry knowledge.

Contribution

It offers a self-contained, accessible introduction to Lie group methods for differential equations, emphasizing local transformation groups and their integrability.

Findings

Introduces local transformation group theory for differential equations

Explains the Stefan-Sussman integrability condition

Provides foundational knowledge for symmetry analysis

Abstract

These are lecture notes of a course on symmetry group analysis of differential equations, based mainly on P. J. Olver's book 'Applications of Lie Groups to Differential Equations'. The course starts out with an introduction to the theory of local transformation groups, based on the Stefan-Sussman theory on the integrability of distributions of non-constant rank. The exposition is self-contained, pre-supposing only basic knowledge in differential geometry and Lie groups.