Notes on Lie derivatives, algebraic D-varieties, and Ax's theorem

TL;DR

This paper explores the connection between Lie derivatives, algebraic D-varieties, and Ax's theorem, providing insights into differential equations on algebraic structures and offering an accessible introduction for students.

Contribution

It clarifies the relationship between Lie derivatives and differential equations on algebraic D-varieties and presents an accessible account of Ax's theorem.

Findings

Elucidates the link between Lie derivatives and differential equations on cotangent spaces.

Provides an accessible explanation of Ax's theorem for students.

Discusses the role of sharp points in algebraic D-varieties.

Abstract

We discuss the relationship between Lie derivatives and the linear differential equations on cotangent spaces of algebraic D-varieties at sharp points. We also take the liberty to give an account of Ax's theorem (which may be useful as an entry point to the subject for students).