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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (10): 79-84.doi: 10.6040/j.issn.1671-9352.0.2019.192

• • 上一篇    

三角代数上互逆元处的高阶ξ-Lie可导映射

张霞,张建华*   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710062
  • 发布日期:2019-10-12
  • 作者简介:张霞(1993— ), 女, 硕士研究生, 研究方向为算子代数. E-mail:15529091178@163.com*通信作者简介:张建华(1965— ),男, 博士, 教授, 博士生导师, 研究方向为算子代数. E-mail:jhzhang@snnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(11471199)

Higher ξ-Lie derivable maps on triangular algebras at reciprocal elements

ZHANG Xia, ZHANG Jian-hua*   

  1. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Published:2019-10-12

摘要: 设U=Tri(A,M,B )是含单位元1的三角代数,1A、1B分别是A和B的单位元。对任意的A∈A, B∈B分别存在整数k1、k2,使得k11A-A, k21B-B在三角代数中可逆。利用代数分解的方法,证明了如果{φn}n∈N:U→U是一列线性映射满足对任意的U,V∈U且UV=VU=1,有φn([U,V]ξ)=∑i+j=nφi(U)φj(V)-ξφi(V)φj(U)(ξ≠0,1),则{φn}n∈N是U上的高阶导子,其中φ0=id0是恒等映射,[U,V]ξ=UV-ξVU。

关键词: 三角代数, 高阶ξ-Lie可导映射, 高阶导子

Abstract: Let U=Tri(A,M,B )be a triangular algebra with identity 1, 1A,1B be the unit of A and B, respectively. For any A∈A, B∈B, there are integers k1,k2 respectively, making k11A-A, k21B-B invertible in triangular algebras. n}n∈N:U→U be a sequence of linear maps. In this paper, we prove that if {φn}n∈N satisfies φn([U,V]ξ)=∑i+j=nφi(U)φj(V)-ξφi(V)φj(U)(ξ≠0,1), for any U,V∈U with UV=VU=1, then n}n∈N is a higher derivation, where φ0=id0 is the identity map, [U,V]ξ=UV-ξVU.

Key words: triangular algebra, higher ξ-Lie derivable map, higher derivation

中图分类号: 

  • O177.1
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