Definition 1

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

Lie Groups and Lie Algebras, chapter I, § 4. Nilpotent Lie algebras

A Lie algebra $g$ is called nilpotent if there exists a decreasing finite sequence of ideals $(g_i)_{1 \leq i \leq p}$ of $g$ with $g_0 = g, g_p = \{0\}$ , such that $[g, g_i] \subset g_{i+1}$ for $0 \leq i < p$ .

A commutative Lie algebra is nilpotent.

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

Cited by

Proposition 1, § 4
Proposition 2, § 4
Proposition 6, § 2

Cites

Nothing.