The Lie algebra of polynomial vector fields on the affine space is 2-generated

2025/11/29 by Ivan Beldiev, Beldiev, Ivan
Mathematics · #Advanced Differential Equations and Dynamical Systems #Holomorphic and Operator Theory #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2512.00604

Abstract

We prove that the infinite-dimensional Lie algebra of polynomial vector fields on the affine space \KKⁿ is generated by two explicitly given elements.

Citations

• On complete generators of certain Lie algebras on Danielewski surfaces
• On nilpotent generators of the symplectic Lie algebra
• Lie algebras of vector fields on smooth affine varieties

Related

• Integrable generators of Lie algebras of vector fields on ℂⁿ
• Integrable generators of Lie algebras of vector fields on SL₂(ℂ) and on xy = z²
• On complete generators of certain Lie algebras on Danielewski surfaces
• Lie algebras of vector fields on smooth affine varieties
• Lie Algebras of vector fields on convenient manifolds