Corollary 1

Tag 01IZ, permanent. Cite it as [Bourbaki, Tag 01IZ].

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

$\mathfrak{g}$ is simple if and only if R is irreducible (in other words, its Dynkin graph is connected).

This follows from Prop. 6.

A Lie algebra $\mathfrak{a}$ is said to be absolutely simple if, for every extension $k'$ of $k$ , the $k'$ -Lie algebra $\mathfrak{a}_{(k')}$ is simple.

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

§ 13. Classical splittable simple Lie algebras
Corollary 2, § 3
Scholium, § 4

Cites

Prop. 6