Consider the algebra (I am for forgetting the Hopf structure) $U_q(\frak{sl}_2)$ defined over ${\mathbb C}$, and the formal power series version/ $h$adic version $U_h(\frak{sl}_2)$, which I think as the complex algebra freely by the elements $E,F,H$, completed with respect to the usual $h$adic metric, and quotiented by the closure of the ideal generated by the usual set of generators. Now if I take the complex formal power series algebra of $U_q(\frak{sl}_2)$, ie the trivial deformation, then how will this relate to $U_h(\frak{sl}_2)$? It seems to me that they will be isomorphic, assuming one can somehow relate $h$ and $q$.
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