A class of infinite dimensional simple Lie algebras

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	A class of infinite dimensional simple Lie algebras
	Zhao, KM
	2000-08-01
发表期刊	JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
ISSN	0024-6107
卷号	62 页码:71-84
摘要	Let A be an abelian group, F be a field of characteristic 0, and alpha, beta be linearly independent additive maps from A to F, and let delta epsilon ker(alpha)\{0}. Then there is a Lie algebra L = L(A, alpha, beta, delta) = circle plus(x epsilon A) Fe-x under the product [e(x), e(y)] = alpha(x - y) e(x+y)+(alpha boolean AND beta) (x, y) e(x+y-delta). If, further, beta(delta) = 1, and beta(A) = Z, there is a subalgebra L+ - L(A(+), alpha,beta,delta) = circle plus(x epsilon A) + Fe-x, where A(+) = {x epsilon A / beta(x) greater than or equal to 0} The necessary and sufficient conditions are given for L' = [L, L] and L+ to be simple, and all semi-simple elements in L' and Lf are determined. It is shown that L' and L+ cannot be isomorphic to any other known Lie algebras and L' is not isomorphic to any L+, and all isomorphisms between two L' and all isomorphisms between two L+ are explicitly described.
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000089649600006
出版者	LONDON MATH SOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/15127
专题	中国科学院数学与系统科学研究院
通讯作者	Zhao, KM
作者单位	Chinese Acad Sci, Math Inst, Acad Math & Syst Sci, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhao, KM. A class of infinite dimensional simple Lie algebras[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES,2000,62:71-84.
APA	Zhao, KM.(2000).A class of infinite dimensional simple Lie algebras.JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES,62,71-84.
MLA	Zhao, KM."A class of infinite dimensional simple Lie algebras".JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES 62(2000):71-84.