Corollary

Tag 014C, permanent. Cite it as [Bourbaki, Tag 014C].

Lie Groups and Lie Algebras, chapter VIII, § 7. Finite dimensional modules over a split semi-simple Lie algebra

Let $E,E'$ be finite dimensional $\mathfrak{g}$ -modules. Then E is isomorphic to $E'$ if and only if ch E = ch $E'$ .

This follows from Th. 2 (ii) and the fact that $E,E'$ are semi-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

Nothing.

Cites

Th. 2