Corollary

Tag 00VB, permanent. Cite it as [Bourbaki, Tag 00VB].

Lie Groups and Lie Algebras, chapter VII, § 3. Conjugacy theorems

Let $\mathfrak{h}$ be a nilpotent subalgebra of $\mathfrak{g}$ . The subalgebra $\mathfrak{g}^0(\mathfrak{h})$ has properties (i), (ii), (iii) in Prop. 3.

Indeed, Prop. 11 of §2, no. 3, shows that $\mathfrak{g}^0(\mathfrak{h})$ has property (ii).

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

Exercise 13, § 3

Cites

Prop. 11 of §2, no. 3
Prop. 3