On deformations of the filiform Lie superalgebra $L_{n,m}$

Abstract

In 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.

arXiv comment13 pages

Cited by in corpus (1)

• Solvable Leibniz superalgebras whose nilradical has the characteristic sequence $(n-1,1\mid m)$ and nilindex $n+m$