Corollary

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

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

For all $g \in A^*$ , let $i(g)$ be the automorphism $y \mapsto gyg^{-1}$ of A, so that $i$ is an analytic linear representation of $A^*$ on A. For all $z \in L(A^*) = A, L(i)z$ is the inner derivation $y \mapsto zy - yz$ of A.

This follows from Propositions 49 and 44.

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

Cited by

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Cites

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