Bourbaki

Theorem 2 (H. Weyl)

Tag 09ZL, permanent. Cite it as [Bourbaki, Tag 09ZL].

Lie Groups and Lie Algebras, chapter I, § 6. Semi-simple Lie algebras

Every finite-dimensional linear representation of a semi-simple Lie algebra is completely reducible.

This follows from Lemmas 2 and 3.

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

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Transcribed from the printed volume. Not translated.