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Levi's theorem - Wikipedia, the free encyclopedia

Levi's theorem

From Wikipedia, the free encyclopedia

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Levi's theorem is the following result in mathematics. Let $\mathfrak{g}$ be a complex Lie algebra and $\mathfrak{r}$ its radical (maximal solvable ideal). 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.

This article incorporates material from Levi's theorem on PlanetMath, which is licensed under the GFDL.

This algebra-related article is a stub. You can help Wikipedia by expanding it.

Retrieved from "http://en.wikipedia.org../../../l/e/v/Levi%27s_theorem.html"

Categories: PlanetMath sourced articles | Lie algebras | Mathematical theorems | Algebra stubs

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