Proposition 4

Tag 0A91, permanent. Cite it as [Bourbaki, Tag 0A91].

Lie Groups and Lie Algebras, chapter III, § 2. Group of tangent vectors to a Lie group

*Let $G$ be a Lie group. Then $T(G)$ , with the law of composition tangent to the multiplication of $G$ , is a Lie group. The identity element of $T(G)$ is the vector $0_e$ .

This follows from Propositions 1 and 2.

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

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Cites

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