Quasifinite modules of a Lie algebra related to Block type
type: Item
instance of: scholarly article
title: Quasifinite modules of a Lie algebra related to Block type
zbMATH Open document ID: 1136.17020
author: Qing Wang
author: Shaobin Tan
published in: Journal of Pure and Applied Algebra
publication date: 2007-09-03T00:00:00Z
review text: Let \(\mathcal B\) be the Lie algebra, called a Lie algebra related to Block type, with basis \(\{L_{\alpha,i},\kappa\mid \alpha,i\in{\mathbb{Z}}\), \(i\geq0\}\) and relations \([L_{\alpha,i},L_{\beta,j}]=((i+1)\beta-(j+1)\alpha)L_{\alpha+\beta,i+j}+\delta_{\alpha+\beta,0}\delta_{i+j,0} \frac{\alpha^3-\alpha}{6}\kappa,\) \([\kappa,{\mathcal B}]=0\). The authors prove that any quasifinite irreducible \(\mathcal B\)-module is either highest weight, lowest weight or uniformly bounded. They also construct and classify the \(\mathcal B\)-modules of the intermediate series, and determine the necessary and sufficient condition for an irreducible highest weight module to be quasifinite.
reviewed by: Yucai Su
Mathematics Subject Classification ID: 17B65
Mathematics Subject Classification ID: 17B68
Mathematics Subject Classification ID: 17B70
zbMATH DE Number: 5186650
zbMATH Keywords: quasifinite module
zbMATH Keywords: Lie algebras related to Block type
Wikidata QID: Q115345607
MaRDI profile type: Publication
full work available at URL: j.jpaa.2007.03.005
OpenAlex ID: W1974264227
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DOI: 10.1016/J.JPAA.2007.03.005
description: scientific article; zbMATH DE number 5186650