BiHom-Superdialgebras and Associated BiHom-Leibniz Superalgebras

This paper introduces the notions of BiHom-superdialgebras and BiHom-Leibniz superalgebras, which generalize Hom-superdialgebras and BiHom-dialgebras to the super setting with two commuting homomorphisms. We establish the fundamental properties of these structures and explore their interconnections. Various operators acting on BiHom-superdialgebras, including Rota–Baxter operators, Nijenhuis operators, and averaging operators, are studied, and it is shown that they produce new BiHom-superdialgebra structures. A construction of BiHom-Leibniz superalgebras from regular BiHom-superdialgebras with coinciding products is provided. The notion of BiHom-Poisson superdialgebras is introduced as a simultaneous generalization of BiHom-superdialgebras and BiHom-Leibniz superalgebras. Finally, we develop the theory of actions and semidirect products for BiHom-superdialgebras and prove the compatibility of the Leibniz functor with semidirect products in the purely even case.