Hom-Jordan algebras and their k-(a,b,c)-derivations

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 (k)-(a,b,c)-derivations of Hom-Jordan algebras, and show that the dimension of D-V(alpha k)(a,b,c) is an invariant, the three original parameters of D-V(alpha k)(a,b,c) are in fact reduced to only one. Moreover, we obtain a relationship between D-V(alpha k)(a,b,c) and structure constants.