Remark

Tag 0176, permanent. Cite it as [Bourbaki, Tag 0176].

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

The three conditions of Prop. 1 are equivalent if we assume only that $k=k^2$ (cf. Exerc. 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

Nothing.

Cites

Exerc. 1
Prop. 1