Corollary 1

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

Lie Groups and Lie Algebras, chapter VII, § 2. Cartan subalgebras and regular elements of a Lie algebra

Let $\mathfrak{g}$ be a Lie algebra, $\mathfrak{h}$ a Cartan subalgebra of $\mathfrak{g}$ . If $k$ is infinite, there exists $x\in \mathfrak{h}$ such that $\mathfrak{h}=\mathfrak{g}^0(x)$ .

Indeed, $\mathfrak{h}=\mathfrak{g}^0(\mathfrak{h})$ and we can apply Prop. 9 (ii) of §1.

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

Theorem 1, § 2

Cites

Prop. 9 (ii) of §1