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Classification of Simple Weight Modules over the Schrödinger Algebra

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 Sh 6RH, 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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A classification of simple weight modules over the Schrödinger algebra is given. The Krull and the global dimensions are found for the centralizer ${{C}_{S}}(H)$ (and some of its prime factor algebras) of the Cartan element $H$ in the universal enveloping algebra $S$ of the Schrödinger (Lie) algebra. The simple ${{C}_{S}}(H)$-modules are classified. The Krull and the global dimensions are found for some (prime) factor algebras of the algebra $S$ (over the centre). It is proved that some (prime) factor algebras of $S$ and ${{C}_{S}}(H)$ are tensor homological$/$Krull minimal.

Keywords

17B1017B2017B3516E1016P9016P4016P50weight modulesimple modulecentralizerKrull dimensionglobal dimensiontensor homological minimal algebratensor Krull minimal algebra
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 61 , Issue 1 , 01 March 2018 , pp. 16 - 39
Copyright
Copyright © Canadian Mathematical Society 2018

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