Corollary 2

Tag 00ZW, permanent. Cite it as [Bourbaki, Tag 00ZW].

Lie Groups and Lie Algebras, chapter VIII, § 3. Subalgebras of split semi-simple Lie algebras

A splittable simple Lie algebra is absolutely simple.

This follows from Cor. 1.

If $\mathfrak{g}$ is of type $A_l(l\geq 1)$ or $B_l(l\geq 1)$ or $C_l(l\geq 1)$ or $D_l(l\geq 3),\mathfrak{g}$ is said to be a classical splittable simple Lie algebra. If $\mathfrak{g}$ is of type $E_6, E_7, E_8, F_4$ , or $G_2,\mathfrak{g}$ is said to be an exceptional splittable simple Lie algebra.

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. 1