| DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA |
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| 引用本文： | Chen Caoyu. DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA[J]. 数学年刊B辑(英文版), 1996, 17(2): 199-212 |
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| 作者姓名： | Chen Caoyu |
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| 作者单位： | CHEN CAOYU Department of Mathematics，Shanghai Normal University，Shanghai 200234，China. |
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| 基金项目： | Project supported by the National Natural Science Foundation of Chin |
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| 摘 要： | Let L be an n-dimensional nilpotent Lie algebra with a basis {x1,…,xn}, and every xiacts as a locally nilpotent derivation on algebra A. This paper shows that there exists a setof derivations {y1,…,yn} on U(L) such that (A#U(L))#k[yi,…,yn] is isomorphic to theWeyl algebra An(A). The author also uses the derivations to obtain a necessary and sufficientcondition for a finite dimensional Lie algebra to be nilpotent.
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| 关 键 词： | 交叉乘积 挤压乘积 微分算子代数 WEYL代数 |
| 收稿时间： | 1993-12-19 |
| 修稿时间： | 1994-04-23 |
DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA |
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| Chen Caoyu. DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA[J]. Chinese Annals of Mathematics,Series B, 1996, 17(2): 199-212 |
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| Authors: | Chen Caoyu |
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| Affiliation: | DepartnentofMathematics,ShanghaiNormalUniversity,Shanghai200234,China. |
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| Abstract: | Let $L$ be an $n$-dimensional nilpotent Lie algebra with a basis ${x_1, cdots,x_n},$ and every $x_i$ acts as a locally nilpotent derivation on algebra $A$.This paper shows that there exists a set of derivations ${y_1, cdots, y_n}$ on$U(L)$ such that $(A#U(L))#k[y_1, cdots, y_n]$ is isomorphic to the Weylalgebra $A_n(A).$ The author also uses the derivations to obtain a necessary and sufficientcondition for a finite dimensional Lie algebra to be nilpotent. |
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| Keywords: | Crossed porduct Smash product Derivation Nilpotent Lie algebra Weyl algebra |
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