Integrable generators of Lie algebras of vector fields on $\mathbb{C}^n$

Rafael B. Andrist

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arXiv · 1808.06905

Integrable generators of Lie algebras of vector fields on $\mathbb{C}^n$

Rafael B. Andrist

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Abstract

There exist three vector fields with complete polynomial flows on $\mathbb{C}^n$, $n \geq 2$, which generate the Lie algebra generated by all algebraic vector fields on $\mathbb{C}^n$ with complete polynomial flows. In particular, the flows of these vector fields generate a group that acts infinitely transitive. The analogous result holds in the holomorphic setting.

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Rafael B. Andrist. 2018-08-21. Integrable generators of Lie algebras of vector fields on $\mathbb{C}^n$. https://arxiv.org/abs/1808.06905

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