Remark

Tag 0A4C, permanent. Cite it as [Bourbaki, Tag 0A4C].

Lie Groups and Lie Algebras, chapter II, § 3. Enveloping algebra of the free Lie algebra

Let $X$ be a set and let $\alpha \in \mathbf{N}^{(X)}$ ; the rank of the free $K$ -module $L^\alpha(X)$ is also given by formula (16). This follows immediately from Theorem 2 (b) and Proposition 4 of § 2, no. 6.

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

Cited by

Nothing.

Cites

Proposition 4 of § 2, no. 6
Theorem 2