Some deformations of nilpotent Lie superalgebras

In this paper we study the infinitesimal deformations of the Lie superalgebra L-n,L-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(S-2(L-1(n,m)), L-0(n,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(S-2(L-1(n,m)), L-0(n,m)), giving it explicitly for n >= 2m - 1. (c) 2006 Elsevier B.V. All rights reserved.