三角代数上 Jordan 积为幂等元处的高阶ξ-Lie 可导映射

张霞, 张建华

数学学报 ›› 2020, Vol. 63 ›› Issue (3) : 221-228.

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PDF(369 KB)
数学学报 ›› 2020, Vol. 63 ›› Issue (3) : 221-228. DOI: 10.12386/A2020sxxb0018
论文

三角代数上 Jordan 积为幂等元处的高阶ξ-Lie 可导映射

    张霞, 张建华
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Higher ξ-Lie Derivable Maps on Triangular Algebras by Jordan Product Idempotents

    Xia ZHANG, Jian Hua ZHANG
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摘要

U=Tri(AMB)是三角代数,{φn}n∈NUU是一列线性映射.本文利用代数分解的方法,证明了如果对任意U,VUU?V=P为标准幂等元,有φn([U,V]ξi+j=nφiUφjV)-ξφiVφjU))(ξ≠1),则{φn}n∈N是一个高阶导子,其中φ0=id为恒等映射,U?V=UV+VU为Jordan积,[U,V]ξ=UV-ξVUξ-Lie积.

Abstract

Let U=Tri(A, M, B) be a triangular algebra, and {φn}n∈N:UU be a sequence of linear maps. In this paper, we prove that if {φn}n∈N satisfies φn([U, V]ξ)=Σi+j=n φi(U)φj(V)-ξφi(V)φj(U) for any U, VU with U?V=P being the standard idempotent, then {φn}n∈N is a higher derivation, where φ0=id is the identity map, U?V=UV+VU is the Jordan product and[U, V]ξ=UV-ξVU is the ξ-Lie product.

关键词

三角代数 / 高阶&xi / -Lie可导映射 / 高阶导子

Key words

triangular algebra / higher ξ-Lie derivable map / higher derivation

引用本文

导出引用
张霞, 张建华. 三角代数上 Jordan 积为幂等元处的高阶ξ-Lie 可导映射. 数学学报, 2020, 63(3): 221-228 https://doi.org/10.12386/A2020sxxb0018
Xia ZHANG, Jian Hua ZHANG. Higher ξ-Lie Derivable Maps on Triangular Algebras by Jordan Product Idempotents. Acta Mathematica Sinica, Chinese Series, 2020, 63(3): 221-228 https://doi.org/10.12386/A2020sxxb0018

参考文献

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基金

国家自然科学基金资助项目(11471199)

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