Irreducible modules over the derivation algebras of rational quantum tori
Liu, Gengqiang1; Zhao, Kaiming2,3
Source PublicationJOURNAL OF ALGEBRA
AbstractLet 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.
KeywordRational quantum torus Witt algebra Weight module Irreducible module
Funding ProjectNSERC ; NSF of China[10871192]
WOS Research AreaMathematics
WOS SubjectMathematics
WOS IDWOS:000292533200003
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Document Type期刊论文
Corresponding AuthorLiu, Gengqiang
Affiliation1.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
Recommended Citation
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.
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