CMS/SMC
Canadian Mathematical Society
www.cms.math.ca
Canadian Mathematical Society
  location:  PublicationsjournalsCMB
Publications        
Abstract view

Classification of simple weight modules over the Schrödinger algebra

  • V. V. Bavula,
    Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK
  • T. Lu,
    Department of Pure Mathematics, University of Sheffield, Hicks Building, Sheffield S3 7RH, UK
Format:   LaTeX   MathJax   PDF  

Abstract

A classification of simple weight modules over the Schrödinger algebra is given. The Krull and the global dimensions are found for the centralizer $C_{\mathcal{S}}(H)$ (and some of its prime factor algebras) of the Cartan element $H$ in the universal enveloping algebra $\mathcal{S}$ of the Schrödinger (Lie) algebra. The simple $C_{\mathcal{S}}(H)$-modules are classified. The Krull and the global dimensions are found for some (prime) factor algebras of the algebra $\mathcal{S}$ (over the centre). It is proved that some (prime) factor algebras of $\mathcal{S}$ and $C_{\mathcal{S}}(H)$ are tensor homological/Krull minimal.
Keywords: weight module, simple module, centralizer, Krull dimension, global dimension, tensor homological minimal algebra, tensor Krull minimal algebra weight module, simple module, centralizer, Krull dimension, global dimension, tensor homological minimal algebra, tensor Krull minimal algebra
MSC Classifications: 17B10, 17B20, 17B35, 16E10, 16P90, 16P40, 16P50 show english descriptions Representations, algebraic theory (weights)
Simple, semisimple, reductive (super)algebras
Universal enveloping (super)algebras [See also 16S30]
Homological dimension
Growth rate, Gelfand-Kirillov dimension
Noetherian rings and modules
Localization and Noetherian rings [See also 16U20]
17B10 - Representations, algebraic theory (weights)
17B20 - Simple, semisimple, reductive (super)algebras
17B35 - Universal enveloping (super)algebras [See also 16S30]
16E10 - Homological dimension
16P90 - Growth rate, Gelfand-Kirillov dimension
16P40 - Noetherian rings and modules
16P50 - Localization and Noetherian rings [See also 16U20]
 

© Canadian Mathematical Society, 2017 : https://cms.math.ca/