Extreme modules over the Weyl algebra \(A_ n\)
type: Item
instance of: scholarly article
title: Extreme modules over the Weyl algebra \(A_ n\)
zbMATH Open document ID: 0829.16005
DOI: 10.1007/BF01058631
published in: Ukrainian Mathematical Journal
publication date: 1995-02-19T00:00:00Z
review text: We extend well-known results for Weyl algebras (Bernstein inequality, Bernstein filtration, Hilbert function, dimension and multiplicity of finitely generated modules, Bernstein class of modules, Stafford's theorems, global dimension, and Krull dimension) to the class of generalized Weyl algebras containing the Weyl algebras \(A_n\). We also present new results such as the simplicity of the tensor products of simple modules, the classification of certain classes of simple modules, e.g., of polynomial modules and modules with strong \(D\)-torsion (the latter serve as an analog of the weight modules of simple Lie algebras), the classification of extreme \(A_n\)-modules, and the theorem on the multiplicity of simple \(A_n\)-modules.
Mathematics Subject Classification ID: 16D60
Mathematics Subject Classification ID: 16S32
Mathematics Subject Classification ID: 17B20
Mathematics Subject Classification ID: 16W60
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 16S30
zbMATH DE Number: 713548
zbMATH Keywords: Bernstein inequality
zbMATH Keywords: Weyl algebras
zbMATH Keywords: Bernstein filtration
zbMATH Keywords: finitely generated modules
zbMATH Keywords: global dimension
zbMATH Keywords: Krull dimension
zbMATH Keywords: simplicity
zbMATH Keywords: tensor products of simple modules
zbMATH Keywords: simple Lie algebras
author: V. V. Bavula
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 713548