Corollary

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

Lie Groups and Lie Algebras, chapter VIII, § 2. Root system of a split semi-simple Lie algebra

Every element of the Weyl group of $(\mathfrak{g},\mathfrak{h})$ , operating on $\mathfrak{h}$ , is the restriction to $\mathfrak{h}$ of an elementary automorphism of $\mathfrak{g}$ .

For a converse of this result, see §5, no. 2, Prop. 4.

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

Proposition 5, § 11
Corollary, § 3
Remark, § 5
Proposition 2, § 5
Proposition 4, § 5
Proposition 6, § 5
Corollary 2, § 7
Theorem 1, § 8

Cites

§5, no. 2, Prop. 4