三角代数上Lie积为平方零元的非线性Jordan高阶可导映射

doi:10.6040/j.issn.1671-9352.0.2019.100

《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (12): 50-58.doi: 10.6040/j.issn.1671-9352.0.2019.100

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三角代数上Lie积为平方零元的非线性Jordan高阶可导映射

费秀海¹,戴磊²,朱国卫¹

1. 滇西科技师范学院数理学院, 云南临沧 677099;2. 渭南师范学院数学与统计学院, 陕西渭南 714099

发布日期:2019-12-11
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

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

FEI Xiu-hai¹, DAI Lei², ZHU Guo-wei¹

1. School of Mathematics and Physics, Dianxi Science and Technology Normal University, Lincang 677099, Yunnan, China;
2. School of Mathematics and Statistics, Weinan Normal University, Weinan 714099, Shaanxi, China

Published:2019-12-11

摘要/Abstract

摘要： 设U是一个 2-无挠的三角代数,D ={d_n}_n∈N是U上一个Lie积为平方零元的非线性Jordan高阶可导映射。证明了三角代数U上的每一个Lie积为平方零元的非线性Jordan高阶可导映射都是高阶导子。作为结论的应用,得到套代数或 2-无挠的上三角分块矩阵代数上的每一个Lie积为平方零元的非线性Jordan高阶可导映射都是高阶导子。

关键词: 三角代数, 高阶导子, Jordan 高阶导子, 平方零元

Abstract: Let U be a 2-torsion free triangular algebra, D={d_n}_n∈N is a nonlinear Jordan higher derivable map on triangular algebra U by Lie product square zero elements. In this paper, it is shown that every nonlinear Jordan higher derivable map on triangular algebra U by Lie product square zero elements is a higher derivation. As its application, we get that every nonlinear Jordan higher derivable map on a nest algebra or a 2-torsion free block upper triangular matrix algebra U by Lie product square zero elements is a higher derivation.

Key words: triangular algebra, higher derivation, Jordan higher derivation, square zero element

中图分类号:

O177.1

费秀海,戴磊,朱国卫. 三角代数上Lie积为平方零元的非线性Jordan高阶可导映射[J]. 《山东大学学报(理学版)》, 2019, 54(12): 50-58.

FEI Xiu-hai, DAI Lei, ZHU Guo-wei. Nonlinear Jordan higher derivable maps on triangular algebras by Lie product square zero elements[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(12): 50-58.

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三角代数上Lie积为平方零元的非线性Jordan高阶可导映射

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

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