Symbolic algorithms for Lie algebra computation

In [l] a systematic effort to carry out the structural analysis of a Lie algebra L on a computer was begun. The effort concentrated on the calculation of the various radicals of L , the various series of L , a Cartan subalgebra of L , and the derivation algebra of L. From these computations one can determine whether L is nilpotent, solvable, or semisimple. The computer implementations of this analysis were done using APL. This paper describes the extension of this work to the structural analysis of a Lie algebra L whose multiplication table is defined symbolically rather than numerically. The expanded context of this analysis requires a symbol manipulation language for the computer implementations; we have chosen to use MACSYMA.