Remark 6

Tag 0AV3, permanent. Cite it as [Bourbaki, Tag 0AV3].

Lie Groups and Lie Algebras, chapter VI, § 1. Root systems

The Cartan matrix $(n(\alpha, \beta))$ should not be confused with the Coxeter matrix $(m(\alpha, \beta))$ . Note in particular that the Cartan matrix is not necessarily symmetric.

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

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