Highest weight irreducible representations of rank 2 quantum tori

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	Highest weight irreducible representations of rank 2 quantum tori
	Rao, SE ; Zhao, K
	2004-09-01
发表期刊	MATHEMATICAL RESEARCH LETTERS
ISSN	1073-2780
卷号	11 期号:5-6 页码:615-628
摘要	For any nonzero q is an element of C (the complex numbers), the rank 2 quantum torus C-q is the skew Laurent polynomial algebra C[t(1)(+/-1), t(1)(+/-2)] with defining relations: t(2)t(1) = qt(1)t(2) and t(i)t(i)(-1) = t(i)(-1)t(i) = 1. Here we consider C-q as the naturally associated Lie algebra. We add the one dimensional center Ccl and the outer derivation d(1) to C-q to get the extended torus Lie algebra (C) over tilde (q) (and (C) over tilde (q), in a different manner), where we assume q is a primitive m-th root of unity for Cq. Before this paper, there appeared highest weight representations for (C) over tilde (q) and Cq with only positive integral levels. In this paper, we define the highest weight irreducible (Z-graded) module V(phi) over (C) over tilde (q) and (C) over tilde (q) for any linear map phi: C[t(2)(+/-1)] + C-c1 + Cd-1 --> C, thus the central charge (level) can be any complex numbers. We obtain the necessary and sufficient conditions for V(phi) to have finite dimensional weight spaces, thus obtaining a lot of new irreducible weight representations for these Lie algebras. The corresponding irreducible Z x Z-graded modules with finite dimensional weight spaces over (C) over tilde (q) are also constructed.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000226169400006
出版者	INT PRESS BOSTON
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/621
专题	中国科学院数学与系统科学研究院
通讯作者	Rao, SE
作者单位	1.Tata Inst Fundamental Res, Sch Math, Bombay 400005, Maharashtra, India 2.Wilfrid Laurier Univ, Dept Math, Waterloo, ON N2L 3C5, Canada 3.Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Rao, SE,Zhao, K. Highest weight irreducible representations of rank 2 quantum tori[J]. MATHEMATICAL RESEARCH LETTERS,2004,11(5-6):615-628.
APA	Rao, SE,&Zhao, K.(2004).Highest weight irreducible representations of rank 2 quantum tori.MATHEMATICAL RESEARCH LETTERS,11(5-6),615-628.
MLA	Rao, SE,et al."Highest weight irreducible representations of rank 2 quantum tori".MATHEMATICAL RESEARCH LETTERS 11.5-6(2004):615-628.