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arxiv: 2507.22642 · v1 · pith:TOCBEY7Snew · submitted 2025-07-30 · 🧮 math.RT · math.DG

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

Hassan Azad , Indranil Biswas , Ahsan Fazil , Fazal M. Mahomed This is my paper
classification 🧮 math.RT math.DG
keywords classificationfieldsplanesubalgebrasvectorcitecomplexdimensional
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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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  1. Lie's classification of finite dimensional algebras of Vector Fields in C^N

    math.RT 2026-05 unverdicted novelty 1.0

    Outlines brief proofs of Lie's classification for finite dimensional vector field subalgebras in low dimensions and maximal rank algebras in C^N for arbitrary N.