Corollary

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

Lie Groups and Lie Algebras, chapter III, § 3. Passage from a Lie group to its Lie algebra

For all $g \in G$ , $\Delta_G(g) = (\operatorname{mod} \det \operatorname{Ad} g)^{-1}$ . In particular, for $G$ to be unimodular, it is necessary and sufficient that $\operatorname{mod} \det \operatorname{Ad} g = 1$ for all $g \in G$ .

\Delta_G(g) = (\operatorname{mod} \operatorname{Int} g)^{-1} \quad \text{(Integration, Chapter VII, § 1, formula (33))} = (\operatorname{mod} \det L(\operatorname{Int} g))^{-1} \quad \text{(Proposition 55)} = (\operatorname{mod} \det \operatorname{Ad} g)^{-1}.

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

Cited by

Proposition 56, § 3
Corollary 4, § 6

Cites

Integration, Chapter VII, § 1 not yet on this site: INT VII
Proposition 55