三角代数上的局部广义李n导子

Local generalized Lie n derivations on triangular algebras

利用恒等式理论,证明了在一定条件下,三角代数T上的局部广义李n导子δ可以表示为δ=G+h,其中G:T→T为广义导子,h:T→Z(T)满足:对于任意的x_(1),x_(2),…,x_(n)∈T,有h(p_(n)(x_(1),x_(2),…,x_(n)))=0,其中pn为(n-1)-交换子.最后给出了上述结果的一个应用.

Using the identity theory,this paper proves that under certain assumptions,the local generalized Lie n derivation δ on a triangular algebra T is of the form δ=G+h,where G:T→T is a generalized derivation and h:T→Z(T)satisfies h(p_(n)(x_(1),x_(2),…,x_(n)))=0 for all x_(1),x_(2),…,x_(n)∈T,and p_(n) is(n-1)-commutator.The application of this result is presented at the end of this paper.