Definition 6
Tag 0AAB, permanent. Cite it as [Bourbaki, Tag 0AAB].
Lie Groups and Lie Algebras, chapter III, § 3. Passage from a Lie group to its Lie algebra
The normable space , together with the bracket, is called the normable Lie algebra of G, or simply the Lie algebra of G, and is denoted by .
Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.
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