Corollary 2

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

Lie Groups and Lie Algebras, chapter I, § 2. Enveloping algebra of a Lie algebra

If $g$ is a free K-module, the canonical mapping of $g$ into its enveloping algebra is injective.

This follows from Corollary 1 taking $W = T^1$ .

When $g$ is a free K-module (in particular when K is a field), $g$ is identified with a submodule of $U$ under the canonical mapping of $g$ into $U$ . This convention is adopted from the following corollary onwards.

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

Cited by

Nothing.

Cites

Corollary 1