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

TL;DR

This paper proves that the infinite-dimensional Lie algebra of polynomial vector fields on affine space is generated by just two explicitly constructed elements, revealing a surprisingly simple generating set.

Contribution

It establishes that the Lie algebra of polynomial vector fields on affine space is 2-generated, providing explicit generators for this infinite-dimensional algebra.

Findings

The Lie algebra is generated by two explicit elements.

The result applies to polynomial vector fields on affine space.

The algebra is shown to be 2-generated explicitly.

Abstract

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