Simple Lie color algebras of Weyl type

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	Simple Lie color algebras of Weyl type
	Su, YC ; Zhao, KM ; Zhu, LS
	2003
发表期刊	ISRAEL JOURNAL OF MATHEMATICS
ISSN	0021-2172
卷号	137 页码:109-123
摘要	A class of graded simple associative algebras are constructed, and from them, simple Lie color algebras are obtained. The structure of these simple Lie color algebras is explicitly described. More precisely, for an (epsilon, Gamma)-color-commutative associative algebra A with an identity element over a field F of characteristic not 2, and for a color-commutative sub-algebra D of color-derivations of A, denote by A[D] the associative sub-algebra of End(A) generated by A (regarded as operators on A via left multiplication) and D. It is easily proved that, as an associative algebra, A[D] is Gamma-graded simple if and only if A is Gamma-graded D-simple. Suppose A is Gamma-graded D-simple. Then, (a) A[D] is a free left A-module; (b) as a Lie color algebra, the subquotient [A[D], A[D]]/Z(A[D]) boolean AND [A[D], A[D]] is simple (except one minor case), where Z(A[D]) is the color center of A[D].
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics
WOS记录号	WOS:000221618100004
出版者	MAGNES PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/18560
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	1.Chinese Acad Sci, Acad Math & Syst Sci, Beijing 100080, Peoples R China 2.Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China 3.Shanghai Jiao Tong Univ, Dept Math, Shanghai 200030, Peoples R China
推荐引用方式 GB/T 7714	Su, YC,Zhao, KM,Zhu, LS. Simple Lie color algebras of Weyl type[J]. ISRAEL JOURNAL OF MATHEMATICS,2003,137:109-123.
APA	Su, YC,Zhao, KM,&Zhu, LS.(2003).Simple Lie color algebras of Weyl type.ISRAEL JOURNAL OF MATHEMATICS,137,109-123.
MLA	Su, YC,et al."Simple Lie color algebras of Weyl type".ISRAEL JOURNAL OF MATHEMATICS 137(2003):109-123.