三角代数上Jordan高阶导子的刻画

刘丹, 张建华

数学学报 ›› 2016, Vol. 59 ›› Issue (4) : 461-468.

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PDF(361 KB)
数学学报 ›› 2016, Vol. 59 ›› Issue (4) : 461-468. DOI: 10.12386/A2016sxxb0044
论文

三角代数上Jordan高阶导子的刻画

    刘丹, 张建华
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Characterization of Jordan Higher Derivations on Triangular Algebras

    Dan LIU, Jian Hua ZHANG
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摘要

U=Tri(A,M,B)是含单位元I的三角代数,φ={φn}n∈NU上一簇线性映射.本文证明了:如果对任意U,VUUV=VU=I,有φn(UV+VU)=∑i+j=n(φi(U)φj(V)+φi(V)φj(U)),则φ={φn}n∈NU上高阶导子.作为应用,得到了套代数上Jordan高阶导子的一个刻画.

Abstract

Let U=Tri(A, M, B) be the triangular algebra with identity I, and let φ={φn}n∈N be a family of linear maps on U. We show that if φ={φn}n∈N satisfying φn(UV+VU)=∑i+j=n(φi(U)φj(V)+φi(V)φj(U)) whenever U, VU with UV=VU=I, then it is a higher derivation. As its application, we give a different characterization of Jordan higher derivations on nest algebras.

关键词

三角代数 / Jordan高阶导子 / 高阶导子

Key words

Triangular algebra / Jordan higher derivation / higher derivation

引用本文

导出引用
刘丹, 张建华. 三角代数上Jordan高阶导子的刻画. 数学学报, 2016, 59(4): 461-468 https://doi.org/10.12386/A2016sxxb0044
Dan LIU, Jian Hua ZHANG. Characterization of Jordan Higher Derivations on Triangular Algebras. Acta Mathematica Sinica, Chinese Series, 2016, 59(4): 461-468 https://doi.org/10.12386/A2016sxxb0044

参考文献

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基金

国家自然科学基金资助项目(11471199);陕西师范大学研究生培养创新基金(2015CXB007)

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