The classification of simple Lie algebras over the complex numbers is well known. There are four infinite families (types A, B, C, D) corresponding to the Lie algebras sl(n+1,C), so(2n+1,C), sp(2n,C), so(2n,C) respectively, and five exceptional simple Lie algebras, E6, E7, E8, F4, G2.
i1 : simpleLieAlgebra("A",1) o1 = Simple Lie algebra, type A, rank 1 o1 : LieAlgebra |
i2 : simpleLieAlgebra("E",6) o2 = Simple Lie algebra, type E, rank 6 o2 : LieAlgebra |