A complete description of all the infinitesimal deformations of the Lie superalgebra Ln,m

In this paper, we find the dimension and a method to obtain a basis of some infinitesimal deformations of the model Lie superalgebra Ln,m. These deformations lie in Hom(Ln∧V1,V1) being Ln and V1 the even and odd parts of the Lie superalgebra Ln,m respectively. As Ln corresponds to the model filiform Lie algebra, then these deformations can also be identified with the space of the infinitesimal deformations of the filiform Ln-module V1. Combining with Bordemann et al. (2007) [2], Gómez et al. (2008) [3] and Khakimdjanov and Navarro [4] we therefore obtain a complete classification of all the infinitesimal deformations of the model Lie superalgebra Ln,m.