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
Canonical name	LevisTheorem
Date of creation	2013-03-22 13:51:15
Last modified on	2013-03-22 13:51:15
Owner	bwebste (988)
Last modified by	bwebste (988)
Numerical id	5
Author	bwebste (988)
Entry type	Theorem
Classification	msc 17B05