三角代数上部分ξ-Lie可导映射的刻画

A characterization of partial ξ-Lie derivable maps on triangular algebras

运用代数分解方法研究了三角代数U=Tri(A,M,B)上的部分ξ-Lie可导映射.证明了如果对任意A∈A存在整数k使得kIA-A可逆,则U上的线性映射为导子当且仅当它是部分ξ-Lie可导映射.作为应用,证明了非平凡套代数上的线性映射是内导子当且仅当其为部分ξ-Lie可导映射.

Using method of algebra decomposition, partial ξ-Lie derivable map on a triangular algebra u=-Tri（A,M,B） is studied. It is proved that if for every A∈ A, there exists a integer k such that kIA--A is invertible,then a linear map on Uis a derivation if and only if it is a partial ξ-Lie derivable map. As an application, it is proved that inner derivations on nontrivial nest algebras and partialξ-Lie derivable maps are the same.