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The universal enveloping algebra of the Schrödinger algebra and its prime spectrum

  • V. V. Bavula,
    Department of Pure Mathematics, University of Sheffield , Hicks Building , Sheffield , S3 7RH , UK
  • T. Lu,
    School of Mathematical Sciences, Huaqiao University , Quanzhou, Fujian 362021, China
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Abstract

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'.
Keywords: prime ideal, weight module, simple module, centralizer, Whittaker module prime ideal, weight module, simple module, centralizer, Whittaker module
MSC Classifications: 17B10, 16D25, 16D60, 16D70, 16P50 show english descriptions Representations, algebraic theory (weights)
Ideals
Simple and semisimple modules, primitive rings and ideals
Structure and classification (except as in 16Gxx), direct sum decomposition, cancellation
Localization and Noetherian rings [See also 16U20]
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]
 

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