Multiplicity-one representations of divergence-free Lie algebras
type: Item
instance of: scholarly article
title: Multiplicity-one representations of divergence-free Lie algebras
zbMATH Open document ID: 1254.17007
author: Ling Chen
published in: Journal of Algebra
publication date: 2012-07-13T00:00:00Z
review text: In this work, the author considers a special class of \(S\)-modules, where \(S\) is a graded generalized divergence-free Lie algebra according to the Đokovic-Zhao approach [\textit{D. Z. Đoković} and \textit{K. Zhao}, ``Generalized Cartan type \(S\) Lie algebras in characteristic zero'', J. Algebra 193, No. 1, 144--179 (1997; Zbl 0978.17015)]. The main result of the paper is the classification of indecomposable graded \(S\)-modules with the property that their homogeneous components have dimension \(0\) or \(1\). The five classes of indecomposable modules over a generalized Witt algebra with 1-dimensional weight spaces and their restriction to the \(S\) algebras play an central role in this classification [\textit{K. Zhao}, ``Weight modules over generalized Witt algebras with 1-dimensional weight spaces'', Forum Math. 16, No. 5, 725--748 (2004; Zbl 1069.17002)].
Mathematics Subject Classification ID: 17B10
Mathematics Subject Classification ID: 17B65
zbMATH DE Number: 6055209
zbMATH Keywords: diverge-free Lie algebra
zbMATH Keywords: Cartan type
zbMATH Keywords: graded modules
zbMATH Keywords: irreducible modules
zbMATH Keywords: classification
reviewed by: Rutwig Campoamor Stursberg
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2011.12.005
OpenAlex ID: W2013930576
Wikidata QID: Q115351146
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DOI: 10.1016/J.JALGEBRA.2011.12.005
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description: scientific article; zbMATH DE number 6055209