Some deformations of nilpotent Lie superalgebras

In this paper we study the infinitesimal deformations of the Lie superalgebra Ln,mLn,m. By means of these deformations all filiform Lie superalgebras can be obtained. In particular, we give a method that will allow us to determine the dimension of the space of deformations of type Hom(S2(L1n,m),L0n,m). Note that this type of deformation is the only one that occurs for Lie superalgebras which are not Lie algebras. Furthermore we develop a method for calculating a basis of the aforementioned space of deformations Hom(S2(L1n,m),L0n,m), giving it explicitly for n≥2m−1n≥2m−1.