Proposition 7

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

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

Let $G$ be a finite-dimensional Lie group, $g$ its Lie algebra and $a$ a subset of $g$ . Then $Z_G(a)$ is a Lie subgroup of $G$ with Lie algebra $\mathfrak{z}_g(a)$ .

This follows from § 3, Proposition 44 and Corollary 2 to Proposition 39.

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

Cited by

Proposition 9, § 9
Corollary, § 2

Cites

Corollary 2 to Proposition 39
§ 3, Proposition 44