Vector fields invariant under a linear action of a compact Lie group

Richard Cushman

Published 2021-06-27Version 1

This note shows that the module of smooth vector fields on ${\mathbb{R}}^n$, which are invariant under the linear action of a compact Lie group $G$ is finitely generated by polynomial vector fields on ${\mathbb{R}}^n$ which are invariant under the action of $G$.