Remark

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

Lie Groups and Lie Algebras, chapter VIII, § 3. Subalgebras of split semi-simple Lie algebras

The map which associates $R_+(C)$ to a chamber C of R is injective (Chap. VI, §1, no. 7, Cor. 1 of Prop. 20). Consequently, $C \rightarrow \mathfrak{h}+\mathfrak{g}^{R_+(C)}$ is a bijection from the set of chambers of R to the set of Borel subalgebras of $(\mathfrak{g},\mathfrak{h})$ . Thus, the number of Borel subalgebras of $(\mathfrak{g},\mathfrak{h})$ is equal to the order of the Weyl group of R (Chap. VI, §1, no. 5, Th. 2).

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

Nothing.

Cites

Chap. VI, §1, no. 7, Cor. 1 of Prop. 20 not in this corpus
Chap. VI, §1, no. 5, Th. 2 not in this corpus