The universal enveloping algebra of the Schrödinger algebra and its prime spectrum
The prime, completely prime, maximal and primitive spectra are
classified for the universal enveloping algebra of the Schrödinger
algebra. For all of these ideals their explicit generators are
given. A counterexample is constructed to the conjecture of Cheng
and Zhang about non-existence of simple singular Whittaker modules
for the Schrödinger algebra (and all such modules are classified).
It is proved that the conjecture holds 'generically'.
prime ideal, weight module, simple module, centralizer, Whittaker module
17B10 - Representations, algebraic theory (weights)
16D25 - Ideals
16D60 - Simple and semisimple modules, primitive rings and ideals
16D70 - Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
16P50 - Localization and Noetherian rings [See also 16U20]