三角代数上的ξ-Lie可乘映射

齐霄霏;侯晋川;

数学学报 ›› 2009 ›› Issue (03) : 181-186.

数学学报 ›› 2009 ›› Issue (03) : 181-186. DOI: 10.12386/A2009sxxb0071
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三角代数上的ξ-Lie可乘映射

    齐霄霏;侯晋川;
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ξ-Lie Multiplicative Maps on Triangular Algebras

    Xiao Fei QI School of Mathematical Sciences,Shanxi University,Taiyuan 030006,P.R.China Jin Chuan HOU Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,P.R.China School of Mathematical Sciences,Shanxi University,Taiyuan 03000,P.R.Ch
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摘要

设U=Tri(A,M,B)是一个三角代数,其中A和B是实数域或复数域F上含单位元的代数,M是一个忠实的左A-模和忠实的右B模,ξ≠0,1.本文证明了U上每个ξ-Lie可乘双射Φ(即Φ(AB-ξBA)=Φ(A)Φ(B)-ξΦ(B)Φ(A)对所有的A,B∈U均成立)都是ξ-Lie环同构.作为应用,得到上三角块矩阵代数和套代数上ξ-Lie可乘双射的完全刻画.

Abstract

Let U = Tri(A,M,B) be a triangular algebra,where A and B are unital algebras over a real or complex field F,and M is a faithful left A-module as well as a faithful right B-module.Forξ≠0,1,we show that everyξ-Lie multiplicative bijective mapΦ:U→U is additive and thus aξ-Lie ring isomorphism.As applications,ξ-Lie multiplicative bijective maps on upper triangular block matrix algebras and Banach space nest algebras are characterized completely.

关键词

ξ-Lie积 / 三角代数 / 套代数

Key words

nest algebras / ξ-Lie product / triangular algebras

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齐霄霏;侯晋川;. 三角代数上的ξ-Lie可乘映射. 数学学报, 2009(03): 181-186 https://doi.org/10.12386/A2009sxxb0071
Xiao Fei QI School of Mathematical Sciences,Shanxi University,Taiyuan 030006,P.R.China Jin Chuan HOU Department of Mathematics,Taiyuan University of Technology,Taiyuan 030024,P.R.China School of Mathematical Sciences,Shanxi University,Taiyuan 03000,P.R.Ch. ξ-Lie Multiplicative Maps on Triangular Algebras. Acta Mathematica Sinica, Chinese Series, 2009(03): 181-186 https://doi.org/10.12386/A2009sxxb0071

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