Example 1

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

Lie Groups and Lie Algebras, chapter I, § 1. Definition of Lie algebras

Let $L$ be an associative algebra over $K$ . The bracket $[x, y] = xy - yx$ is a bilinear function of $x$ and $y$ . It is easily verified that the law of composition $(x, y) \mapsto [x, y]$ on the $K$ -module $L$ makes $L$ into a Lie algebra over $K$ .

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

Cited by

Example 2, § 1
Example 3, § 1
Example 1, § 1

Cites

Nothing.