Corollary 1

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

Lie Groups and Lie Algebras, chapter III, § 6. Real and complex Lie groups

For $E_1$ to be stable under $\varphi$ , it is necessary and sufficient that $E_1$ be stable under $L(\varphi)$ .

It suffices to take $E_1 = E_2$ in Proposition 13.

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

Cited by