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arxiv: 2404.02847 · v1 · pith:FXHUW3CDnew · submitted 2024-04-03 · 🧮 math.RT

Semisimple Algebras of Vector Fields on mathbb{C}³

Sajid Ali , Hassan Azad , Indranil Biswas , Fazal M. Mahomed , Said Waqas Shah This is my paper
classification 🧮 math.RT
keywords mathbbalgebrasfieldssemisimplevectoralgebracanonicalclassification
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A local classification of semisimple algebras of vector fields on $\mathbb{C}^{3}$ is given, using the canonical forms of the Heisenberg algebra and of $sl(2,\mathbb{C})\times sl(2,\mathbb{C})$.

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  1. Lie's classification of finite dimensional algebras of Vector Fields in C^N

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    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.