THE PRIME IDEALS AND SIMPLE MODULES OF THE UNIVERSAL ENVELOPING ALGEBRA U(b x V2)

Let b be the Borel subalgebra of the Lie algebra sl(2) and V-2 be the simple two-dimensional sl(2)-module. For the universal enveloping algebra A:= U(b x V-2) of the semi-direct product b x V-2 of Lie algebras, the prime, primitive and maximal spectra are classified. The sets of completely prime ideals of A are described. The simple unfaithful A-modules are classified and an explicit description of all prime factor algebras of A is given. The following classes of simple U(b x V-2)-modules are classified: the Whittaker modules, the K[X]-torsion modules and the K[E]-torsion modules.