Proposition 15

Let $\mathfrak{a}$ be a reductive Lie algebra, $k'$ an extension of $k$, and $\mathfrak{m}$ a subalgebra of $\mathfrak{a}$. Then $\mathfrak{m}$ is a parabolic (resp. Borel ) subalgebra of $\mathfrak{a}$ if and only if $\mathfrak{m}\otimes_kk'$ is a parabolic (resp. Borel ) subalgebra of $\mathfrak{a}\otimes_kk'$.

This follows immediately from Prop. 14.