Hom-Lie Color Algebras Structures On Lie Color Algebras Sl(v,?) And Osp(v,?)Type

The aim of this dissertation is to introduce two main results about Hom-Lie color algebras,where the abelian group is G=Z2?Z2.In the first part of this dissertation,I derive that matrix representation of sl(V,?)a and osp(V,?)a,where the a belongs to G,and all generators for automorphism groups of simple Lie color algebras sl(V,?)and osp(V,?).The second part of this dissertation focuses on a generalization of Hom-Lie superalgerbas,which are called Hom-Lie color algebras.I prove that Hom-Lie color algebras structures on finite dimensional simple Lie color algebras sl(V,?)and osp(V,?)are trivial.