Remark 2

Tag 0AJR, permanent. Cite it as [Bourbaki, Tag 0AJR].

Lie Groups and Lie Algebras, chapter III, § 9. Commutators, centralizers and normalizers in a Lie group

Let $\mathfrak{g}$ be a complex semi-simple Lie algebra and $\mathfrak{g}_0$ its underlying real Lie algebra. Then Aut $(\mathfrak{g})$ is open in Aut $(\mathfrak{g}_0)$ , for Int $(\mathfrak{g}_0) \subset \mathrm{Aut}(\mathfrak{g})$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Proposition 29, § 9

Cites

Nothing.