JordanDecompositionOfAlgebra[L, e] yields the Jordan decomposition for an element e of a semi-simple Lie algebra L. The result is a list {s, n} where s is the semi-simple element of the L and n the nilpotent element.
The Lie algebra L can be provided either from its structure constants or from the infinitesimal generator representation. When providing the Lie algebra L with its structure constants denote the element e by using the symbol X, e.g. X[4].
The command checks if the Lie algbera L is indeed a semi-simple Lie algebra.
JordanDecompositionOfAlgebra will attempt to give the semisimple and nilpotent coefficient of the decomposition as a linear compination of the base elements of the Lie algebra. If this is not possible Null will be returned instead.
EXAMPLES
Basic Examples 
(2):
