Solution
= Solution
The <one-parameter subgroup> $\gamma_\xi(t)=\exp(t\xi)$ is the integral curve through the identity of $l_\xi$. Its defining initial-value problem is
$$
\dot\gamma_\xi(t)
=l_\xi(\gamma_\xi(t))
=(dL_{\gamma_\xi(t)})_e\xi,
\qquad
\gamma_\xi(0)=e.
$$