Right-invariant vector field
= Right-invariant vector field
{title2=$r_\xi(g)=(dR_g)_e\xi$}
The right-invariant <vector field> associated with a <Lie algebra> element $\xi$ is obtained by right translation of its value at the identity. Its flow is $g\mapsto\exp(t\xi)g$, hence consists of <left translations on a Lie group>. Right invariance follows because left and right multiplication commute.