Verma Modules over Quantum Torus Lie Algebras

doi:10.4153/CJM-2010-022-1

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	Verma Modules over Quantum Torus Lie Algebras
	Lue, Rencai 1; Zhao, Kaiming 2,3
	2010-04-01
发表期刊	CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES
ISSN	0008-414X
卷号	62 期号:2 页码:382-399
摘要	Representations of various one-dimensional central extensions of quantum tori (called quantum torus Lie algebras) were studied by several authors. Now we define a central extension of quantum tori so that all known representations can be regarded as representations of the new quantum torus Lie algebras L(q). The center of L(q) now is generally infinite dimensional. In this paper, Z-graded Verma modules (V) over tilde(phi) over L(q) and their corresponding irreducible highest weight modules V(phi) are defined for some linear functions phi. Necessary and sufficient conditions for V(phi) to have all finite dimensional weight spaces are given. Also necessary and sufficient conditions for Verma modules (V) over tilde(phi) to be irreducible are obtained.
DOI	10.4153/CJM-2010-022-1
语种	英语
资助项目	NSERC ; NSF of China[10431040] ; NSF of China[10601057]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000275983400008
出版者	CANADIAN MATHEMATICAL SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/10291
专题	中国科学院数学与系统科学研究院
通讯作者	Lue, Rencai
作者单位	1.Suzhou Univ, Dept Math, Suzhou 215006, Jiangsu, Peoples R China 2.Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada 3.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Lue, Rencai,Zhao, Kaiming. Verma Modules over Quantum Torus Lie Algebras[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,2010,62(2):382-399.
APA	Lue, Rencai,&Zhao, Kaiming.(2010).Verma Modules over Quantum Torus Lie Algebras.CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES,62(2),382-399.
MLA	Lue, Rencai,et al."Verma Modules over Quantum Torus Lie Algebras".CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES 62.2(2010):382-399.