三角代数上的Lie n-中心化子  

Lie n-centralizers on triangular algebras

作　　者：刘卓 袁鹤 LIU Zhuo;YUAN He(College of Mathematics and Computer,Jilin Normal University,Siping Jilin 136000)

机构地区：[1]吉林师范大学数学与计算机学院,吉林四平136000

出　　处：《宁夏师范学院学报》2023年第7期5-9,共5页Journal of Ningxia Normal University

摘　　要：设T是三角代数,若线性映射∅:T→T,对任意的x_(1),x_(2),…,x_(n)∈T,当x_(1)x_(2)=0时,满足∅(p_(n)(x_(1),x_(2),…,x_(n)))=p_(n)(∅(x_(1)),x_(2),…,x_(n)),则存在λ∈Z(T)及线性映射τ:T→Z(T),使得对任意x∈T,有∅(x)=λx+τ(x),其中τ当x_(1)x_(2)=0时,满足τ(p_(n)(x_(1),x_(2),…,x_(n)))=0.Let T be a triangular algebra.If there is a linear mapping∅:T→T,for any x_(1),x_(2),…,x_(n)∈T,when x_(1)x_(2)=0 and the condition∅(p_(n)(x_(1),x_(2),…,x_(n)))=p_(n)(∅(x_(1)),x_(2),…,x_(n))is satisfied,there existsλ∈Z(T)and a linear mappingτ:T→Z(T),such that for any x∈T,the function∅(x)=λx+τ(x)holds,whereτ(p_(n)(x_(1),x_(2),…,x_(n)))=0 is satisfied for x_(1)x_(2)=0.

关 键 词：三角代数 中心化子 Lie n-中心化子 

分 类 号：O152.5[理学—数学]