Low-dimensional filiform Lie superalgebras

The present work is regarding filiform Lie superalgebras   which is an important type of nilpotent Lie superalgebras. In general, classifying nilpotent Lie superalgebras is at present an open and unsolved problem. Throughout the present work we contribute to the resolution of this wide problem by classifying filiform Lie superalgebras of low dimensions, in particular less or equal to 77. Furthermore we would establish a method that could be applied to obtain similar results for higher dimensions. Thus, this method would mainly consist in using infinitesimal deformations of the model filiform Lie superalgebra.