三角代数上Lie三重导子的刻画

白延丽, 张建华

数学学报 ›› 2017, Vol. 60 ›› Issue (1) : 31-38.

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PDF(326 KB)
数学学报 ›› 2017, Vol. 60 ›› Issue (1) : 31-38. DOI: 10.12386/A2017sxxb0003
论文

三角代数上Lie三重导子的刻画

    白延丽, 张建华
作者信息 +

Characterizations of Lie Triple Derivations on Triangular Algebras

    Yan Li BAI, Jian Hua ZHANG
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摘要

U=Tri(A,M,B)是三角代数.证明了在一般的假设下,如果线性映射δUU,满足对任意的U,V,WUUV=UW=0(或UV=UW=0),有δ([[U,V],W])=[[δU),V],W]+[[U,δV)],W]+[[U,V],δW)],则对任意UU,δU)=φU)+hU),其中φUU是一个导子,线性映射hUZU),满足对任意的U,V,WUUV=UW=0(或UV=UW=0),有h([[U,V],W])=0.

Abstract

Let U=Tri(A, M, B) be a triangular algebra.In this paper, under mild assumptions, we prove that if δ:UU is a linear map satisfying δ([[U, V], W])=[[δ(U), V], W]+[[U, δ(V)], W]+[[U, V], δ(W)], for any U, V, WU with UV=UW=0(resp.UV=UW=0), then δ(U)=Φ(U)+h(U) for any UU, where Φ:UU is a derivation, h:U→Z(U) is a linear map vanishing at second commutators with UV=UW=0(resp.UV=UW=0).

关键词

三角代数 / Lie三重导子 / Jordan积

Key words

triangular algebra / Lie triple derivation / Jordan product

引用本文

导出引用
白延丽, 张建华. 三角代数上Lie三重导子的刻画. 数学学报, 2017, 60(1): 31-38 https://doi.org/10.12386/A2017sxxb0003
Yan Li BAI, Jian Hua ZHANG. Characterizations of Lie Triple Derivations on Triangular Algebras. Acta Mathematica Sinica, Chinese Series, 2017, 60(1): 31-38 https://doi.org/10.12386/A2017sxxb0003

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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