Abstract: We used the differential complex to calculate the standard cohomology of 4-dimensional even centers and 3-dimensional odd centers Heisenberg Lie superalgebras with coefficients in the 1-dimensional trivial modules. Firstly, we calculated the differential operators of these two classes of Heisenberg Lie superalgebras. Secondly, we calculated the standard cohomology of these two types of Heisenberg Lie superalgebras with coefficients in the 1-dimensional trivial modules. In particular, we obtained the basis and dimension of the standard cohomology for these two types of Heisenberg Lie superalgebras.

Key words: Lie superalgebra, Heisenberg Lie superalgebra, standard cohomology