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Highest weight modules over pre-exp-polynomial Lie algebras

文献类型：期刊论文

作者Batra, Punita2; Guo, Xiangqian3; Lu, Rencai4; Zhao, Kaiming1,5
刊名JOURNAL OF ALGEBRA
出版日期2009-12-15
卷号322期号:12页码:4163-4180
关键词Pre-exp-polynomial Lie algebra Highest weight module
ISSN号0021-8693
DOI10.1016/j.jalgebra.2009.09.024
英文摘要In this paper, we introduce pre-exp-polynomial Lie algebras which include loop algebras. Virasoro-like algebras and some quantum torus Lie algebras. We study "highest weight" representations of these Z(n+1)-graded Lie algebras. More precisely, we show that nongraded and graded irreducible highest weight modules with the same highest weight simultaneously have all finite-dimensional weight spaces or not, and they have all finite-dimensional weight spaces if and only if the highest weight is an exp-polynomial "highest weight". We also show that non-graded and graded highest weight Verma modules with the same highest weight are simultaneously irreducible or not, and we determine necessary and sufficient conditions for a Verma module to be irreducible. (C) 2009 Elsevier Inc. All rights reserved.
资助项目Natural Sciences and Engineering Research Council of Canada ; NSF of China
WOS研究方向Mathematics
语种英语
WOS记录号WOS:000272091500001
出版者ACADEMIC PRESS INC ELSEVIER SCIENCE
源URL[http://ir.amss.ac.cn/handle/2S8OKBNM/8601]  
专题中国科学院数学与系统科学研究院
通讯作者Zhao, Kaiming
作者单位1.Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada
2.Harish Chandra Res Inst, Allahabad 211019, Uttar Pradesh, India
3.Zhengzhou Univ, Dept Math, Zhengzhou 450001, Henan, Peoples R China
4.Suzhou Univ, Dept Math, Suzhou 215006, Jiangsu, Peoples R China
5.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式
GB/T 7714		 Batra, Punita,Guo, Xiangqian,Lu, Rencai,et al. Highest weight modules over pre-exp-polynomial Lie algebras[J]. JOURNAL OF ALGEBRA,2009,322(12):4163-4180.
APA Batra, Punita,Guo, Xiangqian,Lu, Rencai,&Zhao, Kaiming.(2009).Highest weight modules over pre-exp-polynomial Lie algebras.JOURNAL OF ALGEBRA,322(12),4163-4180.
MLA Batra, Punita,et al."Highest weight modules over pre-exp-polynomial Lie algebras".JOURNAL OF ALGEBRA 322.12(2009):4163-4180.

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来源：数学与系统科学研究院

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