Completeness of left-invariant vector fields
= Completeness of left-invariant vector fields
Every smooth <left-invariant vector field> on a <Lie group> is a <complete vector field>. Translate a local <integral curve of a vector field> through the identity to every other point. The same positive local existence interval works at every initial point, so no maximal <integral curve of a vector field> can have a finite endpoint. Uniqueness then makes the curve through the identity a <one-parameter subgroup>.