Ternary Hom-Jordan algebras induced by Hom-Jordan algebras

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 α^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 α^k-quasiderivation algebra and the α^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 α^k-centroids of ternary Hom-Jordan algebras are also developed in the paper.

Keywords:

• Hom-Jordan algebras
• ternary Hom-Jordan algebras
• generalized derivations
• quasiderivations
• centroid

2010 Mathematics Subject Classifications:

• 17B40
• 17C10
• 17C99

Acknowledgements

The authors would like to thank the referee for valuable comments and suggestions on this article.

Disclosure statement

No potential conflict of interest was reported by the authors.