Bourbaki

Corollary 2

Tag 0A44, permanent. Cite it as [Bourbaki, Tag 0A44].

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

If KK is a field of characteristic 0, L(X)L(X) is the Lie algebra of primitive elements of A(X)A(X).

This follows from Corollary 1 and the Corollary to Proposition 9 of § 1, no. 5.

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

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Cites

Transcribed from the printed volume. Not translated.