套代数上Lie同态的一个局部刻画

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

数学季刊 ›› 2014, Vol. 29 ›› Issue (1): 125-128.doi: 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

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

收稿日期:2013-07-15 出版日期:2014-03-30 发布日期:2023-02-14
作者简介: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.
基金资助:
Supported by the Specialized Research Foundation for the Doctoral Program of Universities and Colleges of China(20110202110002)

A Local Characterization of Lie Homomorphisms of Nest Algebras

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

Received:2013-07-15 Online:2014-03-30 Published:2023-02-14
About author: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.
Supported by:
Supported by the Specialized Research Foundation for the Doctoral Program of Universities and Colleges of China(20110202110002)

摘要/Abstract

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

Abstract: 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.

Key words: nest algebra, Lie product, Lie homomorphism

中图分类号:

O177.1

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.

YANG Miao-xia, ZHANG Jian-hua. A Local Characterization of Lie Homomorphisms of Nest Algebras[J]. Chinese Quarterly Journal of Mathematics, 2014, 29(1): 125-128.

套代数上Lie同态的一个局部刻画

A Local Characterization of Lie Homomorphisms of Nest Algebras

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