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
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i2 : simpleLieAlgebra("E",6)
o2 = Simple Lie algebra, type E, rank 6
o2 : LieAlgebra
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