Hom-Jordan algebras and their \(\alpha^k-(a,b,c)\)-derivations. (English) Zbl 1443.17010
Summary: The purpose of this paper is to study Hom-Jordan algebras. First, we give some methods to construct new Hom-Jordan algebras. Then we get some results of associators and right multiplications for a Hom-Jordan algebra. At last, we study derivations and \(\alpha^k-(a,b,c)\)-derivations of Hom-Jordan algebras, and show that the dimension of \(\mathrm{D}^{\alpha^k}_V(a,b,c)\) is an invariant, the three original parameters of \(\mathrm{D}^{\alpha^k}_V(a,b,c)\) are in fact reduced to only one. Moreover, we obtain a relationship between \(\mathrm{D}^{\alpha^k}_V(a,b,c)\) and structure constants.
Keywords:
\(\alpha^k-(a,b,c)\)-derivations; associators; derivations; Hom-Jordan algebras; right multiplicationsReferences:
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