Filiform color Lie superalgebras

The aim of this work is to generalize nilpotent Lie superalgebras of a very important type, i.e. filiform Lie superalgebras, obtaining the notion of filiform color Lie superalgebras. We have proved the existence of an adapted basis for any GG-grading of the filiform color superalgebras. Also we have proved that in order to obtain the whole class of filiform GG-color Lie superalgebras it is only necessary to determine the infinitesimal deformations of the associated model color superalgebra.