Hom-Jordan Superalgebras And Their α~k-(a,b,c)-derivations

The purpose of this thesis is to study Hom-Jordan superalgebras and their important class of derivations.First,we give some methods to construct new Hom-Jordan superalgebras,at the same time,we get some results of left multi-plication operators and Hom-associators for a Hom-Jordan superalgebra.Next,we study derivations and αk-(a,b,c)-derivations of Hom-Jordan superalgebras,and show that the dimension of DJαk(a,b,c)is an invariant,the three original parameters of DJαk(a,b,c)are in fact reduced to only one.Moreover,we obtain a relationship between DJαk(a,b,c)and structure constants.At last,we lead a notion of super-representations into Hom-Jordan superalgebras,and get some important results of super-representations.