Highest weight modules over pre-exp-polynomial Lie algebras

doi:10.1016/j.jalgebra.2009.09.024

CSpace

	Highest weight modules over pre-exp-polynomial Lie algebras
	Batra, Punita 2; Guo, Xiangqian 3; Lu, Rencai 4; Zhao, Kaiming 1,5
	2009-12-15
发表期刊	JOURNAL OF ALGEBRA
ISSN	0021-8693
卷号	322 期号:12 页码:4163-4180
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.
关键词	Pre-exp-polynomial Lie algebra Highest weight module
DOI	10.1016/j.jalgebra.2009.09.024
语种	英语
资助项目	Natural Sciences and Engineering Research Council of Canada ; NSF of China
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000272091500001
出版者	ACADEMIC PRESS INC ELSEVIER SCIENCE
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/8602
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.