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| DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA |
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Citation： |
Chen Caoyu.DERIVATIONS ON DIFFERENTIAL OPERATOR ALGEBRA AND WEYL ALGEBRA[J].Chinese Annals of Mathematics B,1996,17(2):199~212 |
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Net amount： 763 |
Authors： |
Chen Caoyu; |
Foundation： |
Project supported by the National Natural Science
Foundation of 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 Weyl
algebra $A_n(A).$ The author also uses the derivations to obtain a necessary and sufficient
condition for a finite dimensional Lie algebra to be nilpotent. |
Keywords： |
Crossed porduct, Smash product, Derivation,
Nilpotent Lie algebra,Weyl algebra |
Classification： |
16S30, 16S32 |
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