KMS Of Academy of mathematics and systems sciences, CAS
Irreducible modules over the derivation algebras of rational quantum tori | |
Liu, Gengqiang1; Zhao, Kaiming2,3 | |
2011-08-15 | |
Source Publication | JOURNAL OF ALGEBRA
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ISSN | 0021-8693 |
Volume | 340Issue:1Pages:28-34 |
Abstract | 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. |
Keyword | Rational quantum torus Witt algebra Weight module Irreducible module |
DOI | 10.1016/j.jalgebra.2011.05.029 |
Language | 英语 |
Funding Project | NSERC ; NSF of China[10871192] |
WOS Research Area | Mathematics |
WOS Subject | Mathematics |
WOS ID | WOS:000292533200003 |
Publisher | ACADEMIC PRESS INC ELSEVIER SCIENCE |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/13043 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | 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 |
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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