Overrings of primitive factors of quantum sl(2) Original Research Article

We construct certain completely prime Dixmier algebras which are overrings of primitive factors of quantum sl(2). As in the classical case, these algebras are parametrized by infinitesimal characters corresponding to the half-integers. We also show that all completely prime Dixmier algebras for quantum sl(2) are essentially isomorphic to the algebras we have constructed.