I've got a general question about Lie algebras, which is basically this: Q: What is there to be said about the Lie algebras that can be identified in the universal enveloping algebra of a particular Lie algebra? E.g. if I have a Lie algebra of the form [A,B] = ηB, then I would like to identify all of the Lie algebras that can be found in the algebra generated by A and B with the relation AB - BA = ηB. I would be very happy if someone could direct me to any resources related to this question. I am sorry that the question is somewhat vague, but if something resembling an answer forms in the back of your mind please don't hesitate to post.