Hom-Nijienhuis operator and $T$*-extension of Hom-Lie Superalgebras

In this paper, we study hom-Lie superalgebras. We give the definition of hom-Nijienhuis operators of regualr hom-Lie superalgebras and show that the deformation generated by a hom-Nijienhuis operator is trivial. Moreover, we introduce the definition of $T^{\ast }$-extensions of Hom-Lie superalgebras and show that $T^{\ast }$-extensions preserve many properties such as nilpotency, solvability and decomposition in some sense. We also investigate the equivalence of $T^{\ast }$-extensions.