Corollary

Tag 012T, permanent. Cite it as [Bourbaki, Tag 012T].

Lie Groups and Lie Algebras, chapter VIII, § 6. Modules over a split semi-simple Lie algebra

If V is finite dimensional, the canonical homomorphism $U(\mathfrak{g})\rightarrow$ End(V) is surjective.

This follows from (iv), cf. Algebra, Chap. VIII, §3, no. 3.

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

Algebra, Chap. VIII, §3, no. 3