  In this paper, we study the cup products and Betti numbers over cohomology
superspaces of two-step nilpotent Lie superalgebras with coefficients in the
adjoint modules over an algebraically closed field of characteristic zero. As
an application, we prove that the cup product over the adjoint cohomology
superspaces for Heisenberg Lie superalgebras is trivial and we also determine
the adjoint Betti numbers for Heisenberg Lie superalgebras by means of
Hochschild-Serre spectral sequences.
