Corollary 3

Tag 0AJX, permanent. Cite it as [Bourbaki, Tag 0AJX].

Lie Groups and Lie Algebras, chapter III, § 9. Commutators, centralizers and normalizers in a Lie group

Let $G$ be a real or complex Lie group and $G_0$ its identity component. Suppose that $G_0$ is semi-simple and that $G/G_0$ is finite. Then every finite-dimensional analytic linear representation of $G$ is semi-simple.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Proposition 32, § 9

Cites

Nothing.