Corollary

Tag 01J0, permanent. Cite it as [Bourbaki, Tag 01J0].

Lie Groups and Lie Algebras, chapter VIII, § 5. Automorphisms of a semi-simple Lie algebra

— Let $B$ be a basis of $R$ . The group $\operatorname{Aut}(\mathfrak g,\mathfrak h)$ is isomorphic to the semi-direct product of the groups $\operatorname{Aut}(R,B)$ and $\operatorname{Aut}_0(\mathfrak g,\mathfrak h)$ .

This follows from Prop. 1, Cor. 1 of Prop. 2, and Prop. 4.

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Prop. 1
Cor. 1 of Prop. 2
Prop. 4