Exercise 6, § 5

Assume that $k=\mathbf{R}$ or $\mathbf{C}$. Let G be the Lie group Aut$_0(\mathfrak{g})$. Show that an element $a\in G$ is regular (in the sense of Chap. VII, §4, no. 2) if and only if it satisfies the conditions of Exerc. $5a)$.