Corollary 2

Tag 017K, permanent. Cite it as [Bourbaki, Tag 017K].

Lie Groups and Lie Algebras, chapter VIII, § 11. Classes of nilpotent elements and sl2 -triplets

If rk( $\mathfrak{g}$ ) $=l$ , the number of conjugacy classes, relative to Aut $_e(\mathfrak{g})$ , of non-zero nilpotent elements of $\mathfrak{g}$ is at most $3^l$ .

This follows from Cor. 1, the Cor. of Prop. 2, and the Cor. of Prop. 5.

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

Cor. of Prop. 2
Cor. of Prop. 5
Cor. 1