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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
Affiliation:
Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield, S3 7RH, UK, e-mail : [email protected]
T. Lu
Affiliation:
School of Mathematical Sciences, Huaqiao University, Quanzhou, Fujian 362021, China, e-mail : [email protected]
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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’.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2018

References

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