Exercise 5, § 2

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

Lie Groups and Lie Algebras, VII, 55

Assume that $k$ is of characteristic 0. Let $\mathfrak{g}$ be a Lie algebra, $\mathfrak{r}$ its radical, $\mathfrak{h}$ a Cartan subalgebra of $\mathfrak{g}$ . Show that

\mathfrak{r}= [\mathfrak{g},\mathfrak{r}] + (\mathfrak{h}\cap \mathfrak{r})

(Observe that the image of $\mathfrak{h}$ in $\mathfrak{g}/[\mathfrak{g},\mathfrak{r}]$ contains the centre $\mathfrak{r}/[\mathfrak{g},\mathfrak{r}]$ of $\mathfrak{g}/[\mathfrak{g},\mathfrak{r}].$ )

Solution

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Cited by

Exercise 11, § 3

Cites

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