Exercise 2, § 2

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

Lie Groups and Lie Algebras, VII, 55

Let $e$ be the element of $\mathfrak{s}\mathfrak{l}(2,\mathbf{C})$ . Show that $\mathbf{C}e$ is a maximal

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nilpotent Lie subalgebra of $\mathfrak{s}\mathfrak{l}(2,\mathbf{C})$ , but not a Cartan subalgebra of $\mathfrak{s}\mathfrak{l}(2,\mathbf{C})$ .

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