Corollary 3

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

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 subalgebras of $\mathfrak{g}$ isomorphic to $\mathfrak{s}\mathfrak{l}(2, k)$ is at most $3^l$ .

This follows from Cor. 1, Prop. 1, 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. 5
Prop. 1
Cor. 1