Corollary 1

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

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

The map which associates to any $\mathfrak{s}\mathfrak{l}_2$ -triplet its simple element defines by passage to the quotients a bijection from the set of G-conjugacy classes of $\mathfrak{s}\mathfrak{l}_2$ -triplets to the set of G-conjugacy classes of simple elements.

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

Corollary 2, § 11
Corollary 3, § 11

Cites

Nothing.