Corollary

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

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

Every compact simple real Lie algebra of type $A_n(n\geq 1)$ is isomorphic to $\mathfrak{s}\mathfrak{u}(n+ 1,\mathbf{C})$ .

Indeed, every complex Lie algebra of type $A_n$ is isomorphic to $\mathfrak{s}\mathfrak{l}(n+ 1,\mathbf{C})$ (Chap. VIII, §13, no. 1).

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

Proposition 6, § 3

Cites

Chap. VIII, §13, no. 1