Remark 4

Tag 018P, permanent. Cite it as [Bourbaki, Tag 018P].

Lie Groups and Lie Algebras, chapter VIII, § 12. Chevalley orders

If $\mathfrak{g}$ is semi-simple and $\mathscr{H}= Q(R^{\vee})$ , conditions (i) and (ii) of Def. 3 are equivalent, by Th. 3 (ii), to

(iii) $\mathscr{E}$ is stable under $x^{(n)}$ for all $\alpha \in R, x\in \mathscr{G}^{\alpha}, n\in \mathbf{N}$ .

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

Def. 3
Th. 3