三角代数上的一类非线性局部高阶Jordan三重可导映射

费秀海, 王中华, 张海芳

数学学报 ›› 2021, Vol. 64 ›› Issue (5) : 839-856.

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数学学报 ›› 2021, Vol. 64 ›› Issue (5) : 839-856. DOI: 10.12386/A2021sxxb0070
论文

三角代数上的一类非线性局部高阶Jordan三重可导映射

    费秀海1, 王中华2, 张海芳1
作者信息 +

A Class of Nonlinear Local Higher Jordan Triple Derivable Maps on Triangular Algebras

    Xiu Hai FEI1, Zhong Hua WANG2, Hai Fang ZHANG1
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摘要

U是一个三角代数,φD={dn}n∈N分别是U上的非线性局部Jordan三重可导映射和非线性局部高阶Jordan三重可导映射.本文证明了:如果U是一个2-无挠的三角代数,则φD={dn}n∈N分别是可加的导子和可加的高阶导子.作为结论的应用,得到了套代数或2-无挠的上三角分块矩阵代数上的非线性局部Jordan三重可导映射和非线性局部高阶Jordan三重可导映射分别是可加的导子和可加的高阶导子.

Abstract

Let U be a triangular algebra, φ and D={dn}n∈N be a nonlinear local Jordan triple derivable map and a nonlinear local higher Jordan triple derivable map on U, respectively. It is showed in this paper, if U is 2-torsion free, then φ is an additive derivation and D={dn}n∈N is an additive higher derivation. As its application, we get that a nonlinear local Jordan triple derivable map and a nonlinear local higher Jordan triple derivable map on a nest algebra or a 2-torsion free block upper triangular matrix algebra is an additive derivation and an additive higher derivation, respectively.

关键词

局部高阶 Jordan 三重可导映射 / 高阶导子 / 三角代数

Key words

local higher Jordan triple derivable map / higher derivation / triangular algebra

引用本文

导出引用
费秀海, 王中华, 张海芳. 三角代数上的一类非线性局部高阶Jordan三重可导映射. 数学学报, 2021, 64(5): 839-856 https://doi.org/10.12386/A2021sxxb0070
Xiu Hai FEI, Zhong Hua WANG, Hai Fang ZHANG. A Class of Nonlinear Local Higher Jordan Triple Derivable Maps on Triangular Algebras. Acta Mathematica Sinica, Chinese Series, 2021, 64(5): 839-856 https://doi.org/10.12386/A2021sxxb0070

参考文献

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基金

国家自然科学基金(11901451,11901248);云南省教育厅基础研究基金(2020J0748,2021J0635);云南省2020年学术后备人才培养资助计划项目;临沧市2020年科技创新人才项目

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