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, $T_θ$-extensions and $T^{\ast}_θ$-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 $T^{\ast}_θ$-extension.

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