Simple algebras of Weyl type

被引:14
作者
Su, YC [1 ]
Zhao, KM
机构
[1] Shanghai Jiao Tong Univ, Dept Appl Math, Shanghai 200030, Peoples R China
[2] Chinese Acad Sci, Inst Math, Acad Math & Syst Sci, Beijing 100080, Peoples R China
来源
SCIENCE IN CHINA SERIES A-MATHEMATICS PHYSICS ASTRONOMY | 2001年 / 44卷 / 04期
基金
中国国家自然科学基金;
关键词
simple Lie algebra; simple associative algebra; derivation;
D O I
10.1007/BF02881878
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
Over a field F of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector space A[D] = A circle times F[D] from any pair of a commutative associative algebra A with an identity element and the polynomial algebra F[D] of a commutative derivation subalgebra D of F. We prove that A[D], as a Lie algebra (module its center) or as an associative algebra, is simple if and only if A is D-simple and, A[D] acts faithfully on A. Thus we obtain a lot of simple algebras.
引用
收藏
页码:419 / 426
页数:8
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