arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2209.13201math.RA
收藏

Jordan映射与零Lie积确定代数

Jordan maps and zero Lie product determined algebras

Matej Brešar

发表信息：
Turkish J. Math. 46 (2022), 1691-1698 (special volume dedicated to Vesselin Drensky on his 70th birthday)
阅读 PDF
arXiv 页面 ↗HTML 原文 ↗

摘要：

设$A$是域$F$上的代数，{ \rm char}为$(F)\ne 2$ .如果$A$由$[[A,A],[A,A]]$生成为代数，则对于每个反对称双线性映射$Φ:A\times A\to X$，其中$X$是$F$上的任意向量空间，$Φ(x^2,x)=0 $对所有$x\in A$的条件意味着$Φ(xy,z) +Φ(zx,y) + Φ(yz,x)=0$对所有$x,y,z\in A$。这适用于$A$是否是零李积的问题，也用于证明从$A$到半素代数$B$的Jordan同态是一个同态与一个反同态之和.

英文摘要：

Let $A$ be an algebra over a field $F$ with {\rm char}$(F)\ne 2$. If $A$ is generated as an algebra by $[[A,A],[A,A]]$, then for every skew-symmetric bilinear map $Φ:A\times A\to X$, where $X$ is an arbitrary vector space over $F$, the condition that $Φ(x^2,x)=0 $ for all $x\in A$ implies that $Φ(xy,z) +Φ(zx,y) + Φ(yz,x)=0$ for all $x,y,z\in A$. This is applicable to the question of whether $A$ is zero Lie product determined, and is also used in proving that a Jordan homomorphism from $A$ onto a semiprime algebra $B$ is the sum of a homomorphism and an antihomomorphism.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

↑