ABSTRACT

The purpose of this paper is to study the relationships between a Hom-Jordan algebras and its induced ternary Hom-Jordan algebras. We give some properties of the ${\alpha }^k$-generalized derivation algebra $GDer\left(\mathcal{J}\right)$ of a ternary Hom-Jordan algebras. In particular, we prove that $GDer\left(\mathcal{J}\right)=QDer\left(\mathcal{J}\right)+Q\mathrm{\Gamma }\left(\mathcal{J}\right)$, the sum of the ${\alpha }^k$-quasiderivation algebra and the ${\alpha }^k$-quasicentroid. We also prove that $QDer\left(\mathcal{J}\right)$ can be embedded as derivations in a larger ternary Hom-Jordan algebras. General results on ${\alpha }^k$-centroids of ternary Hom-Jordan algebras are also developed in the paper.

摘要

本文的目的是研究Hom-Jordan代数与其三元Hom-Jordan代数之间的关系。我们给出了${\alpha }^{ķ}$广义导数 $GdË\mathrm{[R}（\mathcal{Ĵ}）$Hom-Jordan代数的概念。特别是，我们证明$GdË\mathrm{[R}（\mathcal{Ĵ}）=问dË\mathrm{[R}（\mathcal{Ĵ}）+问\mathrm{\Gamma }（\mathcal{Ĵ}）$，总和 ${\alpha }^{ķ}$-quasiderivation代数和 ${\alpha }^{ķ}$-准质心。我们还证明$问dË\mathrm{[R}（\mathcal{Ĵ}）$可以作为导数嵌入到更大的三元Hom-Jordan代数中。的一般结果${\alpha }^{ķ}$本文还开发了三元Hom-Jordan代数的重心。