Integrable generators of Lie algebras of vector fields on ℂ n

Abstract

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