摘要
Let L be an n-dimensional nilpotent Lie algebra with a basis{x1…,xn),and every xi acts as a locally nilpotent derivation on algebra A. This paper shows that there exists a set of derivations{y1,…,yn}on U(L) such that (A#U(L))#k{y,1,…,yn] is ismorphic to the Weyl algebra An(A).The author also uses the de4rivations to obtain a necessary and sufficient condition for a finite dimesional Lie algebra to be nilpotent.
Let L be an n-dimensional nilpotent Lie algebra with a basis {x1,…,xn}, and every xi
acts as a locally nilpotent derivation on algebra A. This paper shows that there exists a set
of derivations {y1,…,yn} on U(L) such that (A#U(L))#k[yi,…,yn] is isomorphic to the
Weyl algebra An(A). The author also uses the derivations to obtain a necessary and sufficient
condition for a finite dimensional Lie algebra to be nilpotent.
基金
Project supported by the National Natural Science Foundation of Chin
关键词
交叉乘积
挤压乘积
微分算子代数
WEYL代数
Crossed porduct, Smash product, Derivation, Nilpotent Lie algebra, Weyl algebra
