COMPLETELY PRIME MAXIMAL-IDEALS AND QUANTIZATION

Let g be a complex simple Lie algebra of classical type, U(g) its enve loping algebra. We classify the completely prime maximal spectrum of U (g). We also construct some interesting algebra extensions of primitiv e quotients of U(g) and compute their Goldie ranks, lengths as bimodul es, and characteristic cycles. Finally, we study the relevance of thes e algebras to D. Vogan's program of ''quantizing'' covers of nilpotent orbits O in g.