套代数上Lie同态的一个局部刻画

杨妙霞, 张建华

doi:10.13371/j.cnki.chin.q.j.m.2014.01.015

数学季刊 >

2014 , Vol. 29 >Issue 1: 125 - 128

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2014.01.015

套代数上Lie同态的一个局部刻画

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1. Xianyang Vocational Technical College 2. College of Mathematics and Information Science, Shaanxi Normal University

YANG Miao-xia(1964-), female, native of Xianyang, Shaanxi, a lecturer of Xianyang Vocational Technical College, engages in functional analysis; ZHANG Jian-hua(1965-), male, native of Yongcheng,Henan, a professor of Shaanxi Normal University, Ph.D., engages in operator algebra.

收稿日期: 2013-07-15

网络出版日期: 2023-02-14

基金资助

Supported by the Specialized Research Foundation for the Doctoral Program of Universities and Colleges of China(20110202110002)

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A Local Characterization of Lie Homomorphisms of Nest Algebras

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1. Xianyang Vocational Technical College 2. College of Mathematics and Information Science, Shaanxi Normal University

Received date: 2013-07-15

Online published: 2023-02-14

Supported by

Supported by the Specialized Research Foundation for the Doctoral Program of Universities and Colleges of China(20110202110002)

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摘要

In this paper, linear maps preserving Lie products at zero points on nest algebras are studied. It is proved that every linear map preserving Lie products at zero points on any finite nest algebra is a Lie homomorphism. As an application, the form of a linear bijection preserving Lie products at zero points between two finite nest algebras is obtained.

关键词： nest algebra; Lie product; Lie homomorphism

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杨妙霞, 张建华 . 套代数上Lie同态的一个局部刻画[J]. 数学季刊, 2014 , 29(1) : 125 -128 . DOI: 10.13371/j.cnki.chin.q.j.m.2014.01.015

Abstract

Key words： nest algebra; Lie product; Lie homomorphism

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