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Simple algebras of Weyl type, II
Zhao, KM
2002
Source PublicationPROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
ISSN0002-9939
Volume130Issue:5Pages:1323-1332
AbstractOver 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.
Keywordsimple Lie algebra simple associative algebra derivation
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied ; Mathematics
WOS IDWOS:000173652900010
PublisherAMER MATHEMATICAL SOC
Citation statistics
Cited Times:7[WOS]   [WOS Record]     [Related Records in WOS]
Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/17029
Collection中国科学院数学与系统科学研究院
AffiliationChinese Acad Sci, Acad Math & Syst Sci, Inst Math, Beijing 100080, Peoples R China
Recommended Citation
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.
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