Proposition 8

Tag 0100, permanent. Cite it as [Bourbaki, Tag 0100].

Lie Groups and Lie Algebras, chapter VIII, § 3. Subalgebras of split semi-simple Lie algebras

Let $\mathfrak{b}$ be a subalgebra of $\mathfrak{g},k'$ an extension of $k$ . Then $\mathfrak{b}\otimes_kk'$ is a Borel subalgebra of $(\mathfrak{g}\otimes_kk',\mathfrak{h}\otimes_kk')$ if and only if $\mathfrak{b}$ is a Borel subalgebra of $(\mathfrak{g},\mathfrak{h})$ .

This is clear from condition (iii) of Prop. 7.

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 14, § 3

Cites

Prop. 7