Remark

Tag 0AW0, permanent. Cite it as [Bourbaki, Tag 0AW0].

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

The root

\tilde{\alpha} = \sum_i n_i \alpha_i

in (i) is said to be the highest root of $\mathbf{R}$ (with respect to $C$ ). Note that, by (i), we have $n_i \geq 1$ for all $i$ .

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

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