Hom-nijienhuis Operator And T~*-extensionof Hom-Lie Color

In this paper, we study Hom-Lie color algebra. We give the definition of Hom-Nijienhuis operators of regular Hom-Lie color algebra and show that the deformation generated by a Hom-Nijienhuis operator is trivial. Moreover. we introduce the definition of T*-extensions of Hom-Lie color algebra and show that T*-extensions preserve many properties such as nilpotency, solvability and decomposition in some sense. We also inves-tigate the equivalence of T*-extensions.