Let 𝔤 be a Lie algebraMathworldPlanetmath. Since the sum of any two solvable ideals of 𝔤 is in turn solvable, there is a unique maximal solvable ideal of any Lie algebra. This ideal is called the radicalPlanetmathPlanetmath of 𝔤. Note that 𝔤/rad𝔤 has no solvable ideals, and is thus semi-simple. Thus, every Lie algebra is an extension (http://planetmath.org/Extension) of a semi-simple algebra by a solvable one.

Title radical
Canonical name Radical
Date of creation 2013-03-22 13:51:18
Last modified on 2013-03-22 13:51:18
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 5
Author bwebste (988)
Entry type Definition
Classification msc 17B05