# Levi’s theorem

Let $\mathfrak{g}$ be a complex Lie algebra, $\mathfrak{r}$ its radical. Then the extension $0\to\mathfrak{r\to g\to g/r}\to 0$ is split, i.e., there exists a subalgebra $\mathfrak{h}$ of $\mathfrak{g}$ mapping isomorphically to $\mathfrak{g/r}$ under the natural projection.

Title Levi’s theorem LevisTheorem 2013-03-22 13:51:15 2013-03-22 13:51:15 bwebste (988) bwebste (988) 5 bwebste (988) Theorem msc 17B05