Corollary 2

Tag 0AD7, permanent. Cite it as [Bourbaki, Tag 0AD7].

Lie Groups and Lie Algebras, chapter III, § 4. Passage from Lie algebras to Lie groups

Let G be a Lie group, $\rho$ an analytic linear representation of G and $\phi$ an exponential mapping of G. There exists a neighbourhood V of 0 in $L(G)$ such that

\rho(\phi(x)) = \exp(L(\rho)x)

for all

x \in V

This follows from Proposition 8 and Example 2 of no. 3.

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

Cited by

Corollary 3, § 4
Lemma 1, § 3

Cites

Proposition 8