Deformations of the nondegenerate constant Poisson bracket and antibracket on superspaces of an arbitrary superdimension

We consider {(}anti-{\rm)}Poisson superalgebras with a constant nondegenerate {\rm(}anti{\rm)}bracket realized on smooth Grassmann-valued functions with compact supports in $\mathbb{R}^n$ and find the deformations of these superalgebras and their central extensions.