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Lie algebras contained in Universal Enveloping Algebra

  1. Dec 27, 2012 #1
    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.
  2. jcsd
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