An integral form of the quantized enveloping algebra of sl2 and its completions

We introduce an integral form UU of the quantized enveloping algebra of sl2sl2. The algebra UU is exactly large enough so that the quasi-RR-matrix is contained in a completion of U⊗UU⊗U. We study several completions of the algebra UU, and determine their centers. This study is motivated by a study of integrality properties of the quantum sl2sl2 invariants of links and integral homology spheres.