三角代数上关于内导子空间Lie不变的线性映射

doi:10.6040/j.issn.1671-9352.0.2018.017

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (2): 79-83.doi: 10.6040/j.issn.1671-9352.0.2018.017

• • 上一篇

三角代数上关于内导子空间Lie不变的线性映射

费秀海¹,张建华^2*

1.滇西科技师范学院数学学院, 云南临沧 677099;2.陕西师范大学数学与信息科学学院, 陕西西安 710119

发布日期:2019-02-25
作者简介:费秀海(1980— ), 男, 博士, 副教授, 研究方向为算子代数与算子理论. E-mail:xiuhaifei@snnu.edu.cn*通信作者简介:张建华(1965— ), 男, 教授, 博士生导师, 研究方向为算子代数与算子理论. E-mail:jhzhang@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(11471199,11501419);陕西省自然科学基础研究计划资助项目(2014JQ1015)

Linear maps on triangular algebras for which the space of all inner derivations is Lie invariant

FEI Xiu-hai¹, ZHANG Jian-hua^2*

1. College of Mathematics, Dianxi Science and Technology Normal University, Lincang 677099, Yunnan, China;
2. College of Mathematics and Information Science, Shaanxi Normal University, Xian 710119, Shaanxi, China

Published:2019-02-25

摘要/Abstract

摘要： 设U是一个三角代数且满足π_A(Z(U))=Z(A)和π_B(Z(U))=Z(B ),φ是U上的一个R-线性映射。若ID(U)是关于φ的一个Lie不变子空间,则在U上存在一个Lie导子δ和一个中心元λ使得对任意的x∈U,有φ(x)=δ(x)+λx。

关键词: 三角代数, Lie不变, Lie导子, 内导子

Abstract: Let U be a triangular algebra with π_A(Z(U))=Z(A)and π_B(Z(U))=Z(B ), φ be a R-linear mapping from U into itself. If ID(U)is a Lie invariant subspace for φ, then there exists a Lie derivation δ on U and a center element λ such that φ(x)=δ(x)+λx for all x∈U.

Key words: triangular algebra, Lie invariant, Lie derivation, inner derivation

中图分类号:

O177.1

费秀海,张建华. 三角代数上关于内导子空间Lie不变的线性映射[J]. 《山东大学学报(理学版)》, 2019, 54(2): 79-83.

FEI Xiu-hai, ZHANG Jian-hua. Linear maps on triangular algebras for which the space of all inner derivations is Lie invariant[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(2): 79-83.

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三角代数上关于内导子空间Lie不变的线性映射

Linear maps on triangular algebras for which the space of all inner derivations is Lie invariant

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