Proposition 1

Tag 00V2, permanent. Cite it as [Bourbaki, Tag 00V2].

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

Let $\mathfrak{g}$ be a Lie algebra, $\mathfrak{n}$ a subalgebra of $\mathfrak{g}$ such that ad $_{\mathfrak{g}}x$ is nilpotent for all $x\in \mathfrak{n}$ . Then $e^{ad_{\mathfrak{g}}\mathfrak{n}}$ is a subgroup of Aut $_e(\mathfrak{g})$ .

This follows immediately from Lemma 1 (i).

In particular, if $\mathfrak{n}$ is the nilpotent radical of $\mathfrak{g},e^{ad_{\mathfrak{g}}\mathfrak{n}}$ is the group of special automorphisms of $\mathfrak{g}$ (Chap. I, §6, no. 8, Def. 6).

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

§ 3. Conjugacy theorems

Cites

Chap. I, §6, no. 8, Def. 6 not in this corpus
Lemma 1