Representations of centrally-extended Lie algebras over differential operators and vertex algebras

doi:10.1016/j.jpaa.2007.10.019

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	Representations of centrally-extended Lie algebras over differential operators and vertex algebras
	Xu, Xiaoping
刊名	JOURNAL OF PURE AND APPLIED ALGEBRA
	2008-06-01
卷号	212 期号:6 页码:1253-1309
ISSN号	0022-4049
DOI	10.1016/j.jpaa.2007.10.019
英文摘要	We construct irreducible modules of centrally-extended classical Lie algebras over left ideals of the algebra of differential operators on the circle, through certain irreducible modules of centrally-extended classical Lie algebras of infinite matrices with finite number of nonzero entries. The structures of vertex algebras associated with the vacuum representations of these algebras are determined. Moreover, we prove that under certain conditions, the highest-weight irreducible modules of centrally-extended classical Lie algebras of infinite matrices with finite number of nonzero entries naturally give rise to the irreducible modules of the simple quotients of these vertex algebras. From vertex algebra and its representation point of view, our results with positive integral central charge are high-order differential operator analogues of the well-known WZW models in conformal field theory associated with affine Kac-Moody algebras. Indeed, when the left ideals are the algebra of differential operators, our Lie algebras do contain affine Kac-Moody algebras as subalgebras and our results restricted on them are exactly the representation contents in WZW models. Similar results with negative central charge are also obtained. (C) 2007 Elsevier B.V. All rights reserved.
语种	英语
出版者	ELSEVIER SCIENCE BV
WOS记录号	WOS:000253824000001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/6674]
专题	数学所
通讯作者	Xu, Xiaoping
作者单位	Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Xu, Xiaoping. Representations of centrally-extended Lie algebras over differential operators and vertex algebras[J]. JOURNAL OF PURE AND APPLIED ALGEBRA,2008,212(6):1253-1309.
APA	Xu, Xiaoping.(2008).Representations of centrally-extended Lie algebras over differential operators and vertex algebras.JOURNAL OF PURE AND APPLIED ALGEBRA,212(6),1253-1309.
MLA	Xu, Xiaoping."Representations of centrally-extended Lie algebras over differential operators and vertex algebras".JOURNAL OF PURE AND APPLIED ALGEBRA 212.6(2008):1253-1309.