Irreducible modules over the derivation algebras of rational quantum tori

doi:10.1016/j.jalgebra.2011.05.029

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	Irreducible modules over the derivation algebras of rational quantum tori
	Liu, Gengqiang 1; Zhao, Kaiming 2,3
	2011-08-15
发表期刊	JOURNAL OF ALGEBRA
ISSN	0021-8693
卷号	340 期号:1 页码:28-34
摘要	Let g be the derivation Lie algebra of a rational quantum torus C(q) where q = (qij)(dxd) and all qij are roots of unity. In Lin and Tan (2004) [LT], a class of uniformly bounded irreducible weight modules over g were constructed, which generalized the construction given by Shen (1986) [Sh], Larsson (1992) [L], and Eswara Rao (1996) [E]. These modules look mysterious because of their very unclear weight sets. In this note, we use very simple methods with a very short proof to re-establish all (even stronger) results in Lin and Tan (2004) [LT] and make these mysterious modules crystal clear. A necessary and sufficient condition for two such modules to be isomorphic is also given. (C) 2011 Elsevier Inc. All rights reserved.
关键词	Rational quantum torus Witt algebra Weight module Irreducible module
DOI	10.1016/j.jalgebra.2011.05.029
语种	英语
资助项目	NSERC ; NSF of China[10871192]
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000292533200003
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/13043
专题	中国科学院数学与系统科学研究院
通讯作者	Liu, Gengqiang
作者单位	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100190, Peoples R China 2.Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada 3.Hebei Normal Teachers Univ, Coll Math & Informat Sci, Shijiazhuang 050016, Hebei, Peoples R China
推荐引用方式 GB/T 7714	Liu, Gengqiang,Zhao, Kaiming. Irreducible modules over the derivation algebras of rational quantum tori[J]. JOURNAL OF ALGEBRA,2011,340(1):28-34.
APA	Liu, Gengqiang,&Zhao, Kaiming.(2011).Irreducible modules over the derivation algebras of rational quantum tori.JOURNAL OF ALGEBRA,340(1),28-34.
MLA	Liu, Gengqiang,et al."Irreducible modules over the derivation algebras of rational quantum tori".JOURNAL OF ALGEBRA 340.1(2011):28-34.