I've got a general question about Lie algebras, which is basically this:(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Lie algebras contained in Universal Enveloping Algebra

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