Remark

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

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

Let B be a basis of E and J the matrix of $\phi$ with respect to B. Then $L(G)$ is the set of elements of $\mathscr{L}(E)$ whose matrix X with respect to B satisfies the equation

{}^tX = -JXJ^{-1}.

This follows from Algebra, Chapter IX, § 1, formula (50).

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

*Algebra*, Chapter IX, § 1 not yet on this site: A IX