Homology Of Heisenberg Lie Superalgebras

In this paper,we study the low-dimensional restricted cohomology of restricted Heisenberg Lie superalgebras with coefficients in the 1-dimensional trivial module and study the 1-dimensional restricted cohomology of restricted Heisenberg Lie superalgebras with coefficients in the adjoint module.Firstly,in this paper we give the restricted structures of Heisenberg Lie superalgebras such that they become restricted Lie superalgebras.Secondly,we calculate the 1,2 dimensional restricted cohomology of restricted Heisenberg Lie superalgebras with coefficients in the 1-dimensional trivial module.Finally,in this paper,we study the 1-dimensional restricted cohomology of restricted Heisenberg Lie superalgebras with coefficients in the adjoin module by calculating the restricted outer derivation of the restricted Heisenberg Lie superalgebra.