Structures and Low Dimensional Classifications of Hom-Poisson Superalgebras

Hom-Poisson superalgebras can be considered as a deformation of Poisson superalgebras. We prove that Hom-Poisson superalgebras are closed under tensor products. Moreover, we show that Hom-Poisson superalgebras can be described using only the twisting map and one binary operation. Finally, all algebra endomorphisms on 2-dimensional complex Poisson superalgebras are computed, and their associated Hom-Poisson superalgebras are described explicitly.