Corollary 1
Tag 09WU, permanent. Cite it as [Bourbaki, Tag 09WU].
Lie Groups and Lie Algebras, chapter I, § 4. Nilpotent Lie algebras
The centre of a non-zero nilpotent Lie algebra is non-zero.
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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