Corollary 1

Tag 0AB1, permanent. Cite it as [Bourbaki, Tag 0AB1].

Lie Groups and Lie Algebras, chapter III, § 3. Passage from a Lie group to its Lie algebra

In the notation of Proposition 39, the set of $g \in G$ such that $\pi(g)(E_1) \subset E_1$ is a Lie subgroup of $G$ and its Lie algebra is the set of $a \in L(G)$ such that $L(\pi)a$ maps $E_1$ into $E_1$ .

We apply Proposition 39 with $E_1 = E_2$ .

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

Cited by

Proposition 10, § 9

Cites

Proposition 39