In Arkhipov, Bezrukavnikov and Ginzburg's paper "Quantum Groups, the loop Grassmannian and the Springer resolution", they mentioned that Lusztig introduced a certain completion for universal enveloping algebra $\widehat{U\mathfrak{g}}$, so that the finite dimensional representions $Rep(\widehat{U\mathfrak{g}})$ is isomorphic to $Rep(G)$, where $G$ is the connected semisimple group of adjoint type with lie algebra $\mathfrak{g}$ over algebraically closed field of characteristic zero.

What is the construction of this completion? Any references?