Group like elements of Universal enveloping algebras

MrQG
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I'm working with universal enveloping algebras, specifically U(sl(2)). Does anybody know of a nice way of determining what the group like elements are. Of course, one could go a direct route and compare the coproduct Δ(v), v\in U(sl(2)), directly with the desired outcome v\otimesv, but the resulting equation is not pretty at all.
 
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Anyone? Any thoughts?
 

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