Remark

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

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

$\varpi(x) \cdot (\mathrm{ad}\ x) = \exp \mathrm{ad}\ x - 1$ . We write, by an abuse of notation,

\varpi(x) = \frac{\exp \mathrm{ad}\ x - 1}{\mathrm{ad}\ x}.

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

Cited by

Nothing.

Nothing.