Multipliers,covers,and stem extensions for Lie superalgebras

Suppose that the underlying field is of characteristic different from 2 and 3.We first prove that the so-called stem deformations of a free presentation of a finite-dimensional Lie superalgebra L exhaust all the maximal stem extensions of L,up to equivalence of extensions.Then we prove that multipliers and covers always exist for a Lie superalgebra and they are unique up to superalgebra isomorphisms.Finally,we describe the multipliers,covers,and maximal stem extensions of Heisenberg superalgebras and model filiform Lie superalgebras.