Remark 1

Tag 00U1, permanent. Cite it as [Bourbaki, Tag 00U1].

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

If $\mathfrak{g}\not=\{0\},a_0= 0$ since (ad $x$ ) $(x) = 0$ for all $x\in \mathfrak{g}$ .

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.

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Cites

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