三角代数上互逆元处的高阶ξ-Lie可导映射

doi:10.6040/j.issn.1671-9352.0.2019.192

《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^*

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^*

School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China

Published:2019-10-12

摘要/Abstract

摘要： 设U=Tri(A,M,B )是含单位元1的三角代数,1_A、1_B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k₁1_A-A, k₂1_B-B在三角代数中可逆。利用代数分解的方法,证明了如果{φ_n}_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φ_n(［U,V］_ξ)=∑_i+j=nφ_i(U)φ_j(V)-ξφ_i(V)φ_j(U)(ξ≠0,1),则{φ_n}_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, 1_A,1_B be the unit of A and B, respectively. For any A∈A, B∈B, there are integers k1,k2 respectively, making k₁1_A-A, k₂1_B-B invertible in triangular algebras. {φ_n}_n∈N:U→U be a sequence of linear maps. In this paper, we prove that if {φ_n}_n∈N satisfies φ_n(［U,V］_ξ)=∑_i+j=nφ_i(U)φ_j(V)-ξφ_i(V)φ_j(U)(ξ≠0,1), for any U,V∈U with UV=VU=1, then {φ_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

张霞,张建华. 三角代数上互逆元处的高阶ξ-Lie可导映射[J]. 《山东大学学报(理学版)》, 2019, 54(10): 79-84.

ZHANG Xia, ZHANG Jian-hua. Higher ξ-Lie derivable maps on triangular algebras at reciprocal elements[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(10): 79-84.

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三角代数上互逆元处的高阶ξ-Lie可导映射

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

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