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The Universal Enveloping Algebra of the Schrödinger Algebra and its Prime Spectrum

Published online by Cambridge University Press:  20 November 2018

V. V. Bavula  and
T. Lu
V. V. Bavula
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield, S3 7RH, UK, e-mail : v.bavula@sheffield.ac.uk
T. Lu
Affiliation:
School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China, e-mail : lutao@hqu.edu.cn
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Abstract

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The prime, completely prime, maximal, and primitive spectra are classified for the universal enveloping algebra of the Schrödinger algebra. The explicit generators are given for all of these ideals. A counterexample is constructed to the conjecture of Cheng and Zhang about nonexistence of simple singular Whittaker modules for the Schrödinger algebra (and all such modules are classified). It is proved that the conjecture holds ‘generically’.

Keywords

17B1016D2516D6016D7016P50prime idealweight modulesimple modulecentralizerWhittaker module
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 4 , 01 December 2018 , pp. 688 - 703
Copyright
Copyright © Canadian Mathematical Society 2018

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