Triangle On The Algebra Of Three Yuan Li Guide And Factor On The Von Neumann Algebras Lee Guide Features

This paper introduces some theorems and propsitions about lie tirple derivations of trangular algebras in the first srction,and we introduce several theorems and claims in the second scection about lie derivations of the von Neumann algebras.This paper we give two results in both of the two algebras:Let T be a triangular algebra over a commutative ring R. In this paper, under some mild conditions on T, we prove that if δ:Tâ†'T is an R-linear map satisfying S([[x,y],z])=[[δ(x),y],z]+[[x,8(y)],z]+[[x,y],δ(z)],for any x,y,z∈T, then8=d+Ï„, where d is a derivation of T and Ï„:Tâ†'Z(T)(where Z(T) is the center of T) is an R-linear map vanishing at Lie triple products[[x,y],z].Let R be a factor von Neumann algebra with dimension more than four, In this paper, we prove that if δ:Râ†'R is a linear map satisfying δ([x,y])=[δ(x),y]+[x,δ(y)],for any x,y∈R with xy=0(resp.xy=p, where d is a fixed nontrivial projection of R) then8=d+Ï„, where d is a derivation of R and Ï„:Râ†'CI(where C is the field of complex numbers) is a linear map vanishing at commutators [x,y] with xy=0(resp xy=p).