KMS Of Academy of mathematics and systems sciences, CAS
Simple algebras of Weyl type, II | |
Zhao, KM | |
2002 | |
Source Publication | PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY |
ISSN | 0002-9939 |
Volume | 130Issue:5Pages:1323-1332 |
Abstract | 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. |
Keyword | simple Lie algebra simple associative algebra derivation |
Language | 英语 |
WOS Research Area | Mathematics |
WOS Subject | Mathematics, Applied ; Mathematics |
WOS ID | WOS:000173652900010 |
Publisher | AMER MATHEMATICAL SOC |
Citation statistics | |
Document Type | 期刊论文 |
Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/17029 |
Collection | 中国科学院数学与系统科学研究院 |
Affiliation | Chinese 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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