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

Abstract

A brief proof of Lie's classification of finite dimensional subalgebras of vector fields over the complex plane that have a proper Levi decomposition is given. The proof uses representation theory of sl(2, ℂ). This, combined with [ABMS] and [ABM2] completes the classification of finite dimensional subalgebras of vector fields over the complex plane.