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arXiv · 2507.22642

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

Hassan Azad·Indranil Biswas·Ahsan Fazil·Fazal M. Mahomed
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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.

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Hassan Azad, Indranil Biswas, Ahsan Fazil, Fazal M. Mahomed. 2026-07-30. On Lie's classification of nonsolvable subalgebras of vector fields on the plane. https://arxiv.org/abs/2507.22642

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