Remark 2

Tag 01BC, permanent. Cite it as [Bourbaki, Tag 01BC].

Lie Groups and Lie Algebras, chapter IX, § 3. Compact forms of complex semi-simple Lie algebras

If the complex Lie algebra $\mathfrak{a}=\mathfrak{s}\mathfrak{l}(n,\mathbf{C})$ is equipped with the splitting and Chevalley system introduced in Chap. VIII, §13, no. 1 (IX), then, with the notations in no. 2,

\mathfrak{a}_u=\mathfrak{s}\mathfrak{u}(n,\mathbf{C}),\mathfrak{a}_0=\mathfrak{s}\mathfrak{l}(n,\mathbf{R}),\mathfrak{a}_u\cap \mathfrak{a}_0=\mathfrak{o}(n,\mathbf{R})

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Chap. VIII, §13, no. 1