Hom-Nijienhuis operators and T⁎-extensions of hom-Lie superalgebras

In this paper, we study hom-Nijienhuis operators and T⁎-extensions of hom-Lie superalgebras. We show that a linear map between hom-Lie superalgebras is a morphism if and only if its graph is a hom-subalgebra and show that the infinitesimal deformation generated by a hom-Nijienhuis operator is trivial. Moreover, we introduce the definition of T⁎-extensions of hom-Lie superalgebras and show that T⁎-extensions preserve many properties such as nilpotency, solvability and decomposition in some sense. In particular, we discuss the equivalence of T⁎-extensions using cohomology.