Generalized Cartan Matrix and Non-Semisimple Lie Algebras

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I have a lie algebra whose killing form is degenerate, hence not semi simple by cartan's second criterion.

So I cannot apply a Cartan Weyl Basis to classify the algebra. I currently have an algebra with 5 generators. Later I will have one with 11 generators and I am hoping I can spot how i can continue this to algebras with higher dimension with the method I am using by studying root spaces and dynkin diagrams and so on.

Because the algebra isn't semi-simple, I simply do not have any idea where to start and the literature is all very abstract.

Help :cry:
 
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Anyone? Any help would be good.
 

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