Simple algebras of Weyl type, II

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	Simple algebras of Weyl type, II
	Zhao, KM
	2002
发表期刊	PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN	0002-9939
卷号	130 期号:5 页码:1323-1332
摘要	Over a field F of any characteristic, for a commutative associative algebra A, and for a commutative subalgebra D of Der(F)(A), the vector space A[D] which consists of polynomials of elements in D with coefficients in A and which is regarded as operators on A forms naturally an associative algebra. It is proved that, as an associative algebra, A[D] is simple if and only if A is D-simple. Suppose A is D-simple. Then, (a) A[D] is a free left A-module; (b) as a Lie algebra, the subquotient [A[D], A[D]]/(Z(A[D]) boolean AND [A[D], A[D]]) is simple (except for one case), where Z(A[D]) is the center of A[D]. The structure of this subquotient is explicitly described. This extends the results obtained by Su and Zhao.
关键词	simple Lie algebra simple associative algebra derivation
语种	英语
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied ; Mathematics
WOS记录号	WOS:000173652900010
出版者	AMER MATHEMATICAL 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/17029
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, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
推荐引用方式 GB/T 7714	Zhao, KM. Simple algebras of Weyl type, II[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,2002,130(5):1323-1332.
APA	Zhao, KM.(2002).Simple algebras of Weyl type, II.PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY,130(5),1323-1332.
MLA	Zhao, KM."Simple algebras of Weyl type, II".PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 130.5(2002):1323-1332.