Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras

Abstract

The purpose of this article is to study Bihom-Nijienhuis operators and $T^*$-extensions of Bihom-Lie superalgebras. We show that the deformation generated by a Bihom-Nijienhuis operator is trivial. Moreover, we introduce the definition of $T^*$-extensions of Bihom-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.