Let be a Lie algebra. Since the sum of any two solvable ideals of is in turn solvable, there is a unique maximal solvable ideal of any Lie algebra. This ideal is called the radical of . Note that 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.
|Date of creation||2013-03-22 13:51:18|
|Last modified on||2013-03-22 13:51:18|
|Last modified by||bwebste (988)|