Corollary 2

Tag 011Q, permanent. Cite it as [Bourbaki, Tag 011Q].

Lie Groups and Lie Algebras, chapter VIII, § 5. Automorphisms of a semi-simple Lie algebra

The group $\varepsilon^{-1}(W(R))$ operates simply-transitively on the set of framings of $(\mathfrak{g},\mathfrak{h})$ .

Indeed, Aut( $\mathfrak{g},\mathfrak{h}$ ) operates transitively on the set of framings of $(\mathfrak{g},\mathfrak{h})$ by §4, no. 4, Th. 2. Cor. 2 now follows from Cor. 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

Proposition 5, § 5

Cites

§4, no. 4, Th. 2
Cor. 1