Doubly Z-graded Lie algebras containing a Virasoro algebra

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	Doubly Z-graded Lie algebras containing a Virasoro algebra
	Osborn, JM ; Zhao, KM
	1999-09-01
发表期刊	JOURNAL OF ALGEBRA
ISSN	0021-8693
卷号	219 期号:1 页码:266-298
摘要	In this paper we study Z x Z-graded Lie algebras A = +(i,j is an element of Z)A(i,j) Over a characteristic 0 field F with dim A(i,j) less than or equal to 1 for each i and j, where Z denotes the integers. We shall assume that A satisfies the following three properties: (I) A'(0) = +(i is an element of Z)A(0,i) similar or equal to Vir, the centerless Virasoro algebra; (II) [A(-1,0), A(1,0)] = 0, and ad A(-1,0) and ad A(1,0) act faithfully on the subspace +(i is an element of Z)A(i,1); (III) dim A(+/-1,0) = dim A(0.+/-1) = 1, and A is generated by A(+/-1,0) and A'(0). The main result of the paper is the classification of these algebras. More precisely, A is isomorphic to a simple Block algebra L(a) which has basis {e(i,j) \ (i, j) is an element of Z x Z \ {(- 1/a, 0), (- 2/a, 0)}} and subject to the bracket [GRAPHICS] for some suitable constant a is an element of F\{0, +/- 1, +/- 2}, or is isomorphic to a one- or two-dimensional central extension of L(a) with a is an element of F\{0, +/- 1, +/- 2), or A is isomorphic a one-dimensional derivation extension of L(+/-1) and L(+/-2), or a two-dimensional extension of L(+/-1) by a center element and a derivation. (C) 1999 Academic Press.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000082241400011
出版者	ACADEMIC PRESS INC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/14865
专题	中国科学院数学与系统科学研究院
通讯作者	Osborn, JM
作者单位	1.Univ Wisconsin, Madison, WI 53706 USA 2.Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Osborn, JM,Zhao, KM. Doubly Z-graded Lie algebras containing a Virasoro algebra[J]. JOURNAL OF ALGEBRA,1999,219(1):266-298.
APA	Osborn, JM,&Zhao, KM.(1999).Doubly Z-graded Lie algebras containing a Virasoro algebra.JOURNAL OF ALGEBRA,219(1),266-298.
MLA	Osborn, JM,et al."Doubly Z-graded Lie algebras containing a Virasoro algebra".JOURNAL OF ALGEBRA 219.1(1999):266-298.