2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61432In this work, we recall that every filiform Lie superalgebra is a deformation of the superalgebra $L_{n,m}$. We study the even cocycles which give this nilpotent deformations. A family of independent bilinear maps will help us to describe this cocycles. At the end an evaluation of the dimension of the space $Z_0^2(L_{n,m},L_{n,m})$ is established.13 pagesRings and Algebras17B30;17B56text