Stem Extensions And Covers For Lie Superalgebras

Suppose that the underlying field is of characteristic different from 2,3.In this paper we first prove that the so-called stem deformations of a free presentations 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 Lie superalgebra isomor-phisms.Finally,we describe the multipliers,covers and maximal stem extensions of Heisenberg superalgebras of odd centers and model filiform Lie superalgebras.