可替换-代数上的非线性-Jordan型导子

IF 0.4 Q4 MATHEMATICS Siberian Electronic Mathematical Reports-Sibirskie Elektronnye Matematicheskie Izvestiya Pub Date : 2021-04-23 DOI:10.33048/semi.2022.19.012

A. J. O. Andrade, Gabriela C. Moraes, R. N. Ferreira, B. Ferreira

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引用次数: 1

摘要

设$A$是一个单位替代$*$代数。假设$A$包含一个非平凡对称幂等元$e$，它满足$xA\cdot e=0$意味着$x=0$，$xA\cdot（1_A-e）=0$意味着$x=0$。本文证明了$\Phi$是a上的非线性$*$-Jordan型导数，当且仅当$\Phi$是加法$*$-导数。作为应用，我们得到了关于可替换$W^{*}$-代数的一个结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Nonlinear *-Jordan-type derivations on alternative *-algebras

Let $A$ be an unital alternative $*$-algebra. Assume that $A$ contains a nontrivial symmetric idempotent element $e$ which satisfies $xA \cdot e = 0$ implies $x = 0$ and $xA \cdot (1_A - e) = 0$ implies $x = 0$. In this paper, it is shown that $\Phi$ is a nonlinear $*$-Jordan-type derivation on A if and only if $\Phi$ is an additive $*$-derivation. As application, we get a result on alternative $W^{*}$-algebras.

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