Some deformations of nilpotent Lie superalgebras

Abstract

In this paper we study the infinitesimal deformations of the Lie superalgebra L n , 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 ≥ 2 m − 1 .