Constructions and $T^{\ast }$-Extensions of 3-Bihom-Lie Superalgebras

The aim of this paper is to generalise the construction of $3$-Bihom-Lie superalgebras and we provide some properties can be lifted to its $T^{\ast }$-extensions such as nilpotency, solvability and decomposition. We study the representations, $T_{\theta }$-extensions and $T_{\theta }^{\ast }$-extension of $3$-Bihom-Lie superalgebras and prove the necessary and sufficient conditions for a $2n$-dimensional quadratic $3$-Bihom-Lie superalgebra to be isomorphic to a $T_{\theta }^{\ast }$-extension.