I'd like to set up a Lie algebra from the commutator of a complex Lie algebra. I've found you can create Clifford algebra data with
with(DifferentialGeometry): with(LieAlgebras):
AD:=AlgebraLibraryData("Clifford(3)", Cl3)
How can I set up a Lie algebra through the commutator of the algebra in order to get the LeviDecomposition from that?
I should be able to decompose it? What would be the list of simple Lie algebras it decomposes into?