三角代数上Lie积为平方零元的非线性Jordan可导映射

doi:10.6040/j.issn.1671-9352.0.2017.255

山东大学学报（理学版） ›› 2017, Vol. 52 ›› Issue (12): 42-47.doi: 10.6040/j.issn.1671-9352.0.2017.255

三角代数上Lie积为平方零元的非线性Jordan可导映射

武鹂,张建华^*

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2017-05-22 出版日期:2017-12-20 发布日期:2017-12-22
通讯作者: 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 E-mail:wuli@snnu.edu.cn
作者简介:武鹂(1991— ), 女, 硕士研究生, 研究方向为算子代数. E-mail:wuli@snnu.edu.cn
基金资助:
国家自然科学基金资助项目(11471199)

Nonlinear Jordan derivable maps on triangular algebras by Lie product square zero elements

WU Li, ZHANG Jian-hua^*

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

Received:2017-05-22 Online:2017-12-20 Published:2017-12-22

摘要/Abstract

摘要： 设U=Tri(A, M, B )是特征不为 2 的三角代数, Q={u∈U:u²=0}且φ:U→U是一个映射(无可加或线性假设)。证明了如果对任意a,b∈U且［a,b］∈Q, 有φ(ab)=φ(a)b+aφ(b), 则φ是一个可加导子, 其中［a,b］=ab-ba为Lie积, ab=ab+ba为Jordan积。

关键词: 三角代数, 平方零元, Jordan可导映射

Abstract: Let U=Tri(A, M, B )be a 2-torsion free triangular algebra, and Q={u∈U:u²=0}. We prove that if a map φ:U→U satisfies φ(ab)=φ(a)b+aφ(b)for any a,b∈U with ［a,b］∈Q, then φ is an additive derivation, where ［a,b］=ab-ba is the Lie product and ab=ab+ba is the Jordan product.

Key words: square zero element, triangular algebra, Jordan derivable map

中图分类号:

O177.1

武鹂,张建华. 三角代数上Lie积为平方零元的非线性Jordan可导映射[J]. 山东大学学报（理学版）, 2017, 52(12): 42-47.

WU Li, ZHANG Jian-hua. Nonlinear Jordan derivable maps on triangular algebras by Lie product square zero elements[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 42-47.

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三角代数上Lie积为平方零元的非线性Jordan可导映射

Nonlinear Jordan derivable maps on triangular algebras by Lie product square zero elements

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