Proposition 9

Tag 0AF3, permanent. Cite it as [Bourbaki, Tag 0AF3].

Lie Groups and Lie Algebras, chapter III, § 6. Real and complex Lie groups

*Let $G$ be a complex Lie group and $G'$ the underlying real Lie group. Then $\exp_G = \exp_{G'}$ .

This follows from Proposition 5 of § 4, no. 3 and the analyticity of $\exp_G$ and $\exp_{G'}$ .

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

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