Remark 1

Tag 0AU6, permanent. Cite it as [Bourbaki, Tag 0AU6].

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

Let $k'$ be an extension of $k$ . Identify V canonically with a subset of $V \otimes k'$ and $V^*$ with a subset of $V^* \otimes k' = (V \otimes k')^*$ . Then, R is a root system in $V \otimes k'$ , and the $\alpha^{\sim}$ are the same as before.

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

Cited by

Remark 2, § 1
Proposition 1, § 1

Cites

Nothing.