Remark 2

Tag 00U2, permanent. Cite it as [Bourbaki, Tag 00U2].

Lie Groups and Lie Algebras, chapter VII, § 2. Cartan subalgebras and regular elements of a Lie algebra

Let $k'$ be an extension of $k$ . Write det(T $-$ ad $x'$ ) $=\sum_{i=0}^na'_i(x')T^i$ for $x'\in \mathfrak{g}\otimes_kk'$ . Then $a'_i|\mathfrak{g}=a_i$ for all $i$ .

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 6, § 2

Cites

Nothing.