paper

On Lie's classification of nonsolvable subalgebras of vector fields on the plane

arXiv:2507.22642

Abstract

A brief proof of Lie's classification of finite dimensional subalgebras of vector fields on the complex plane that have a proper Levi decomposition is given. The proof uses basic representation theory of sl(2, C). This, combined with \cite{ABF2} and \cite{ABF3} completes the classification of finite dimensional subalgebras of vector fields on the complex plane.

Final version; to appear in the International Journal of Mathematics