Infinitesimal deformations of filiform Lie algebras of order 3

The Lie algebras of orderFF have important applications for the fractional supersymmetry, and on the other hand the filiform Lie (super)algebras have very important properties into the Lie Theory. Thus, the aim of this work is to study filiform Lie algebras of orderFF which were introduced in Navarro (2014). In this work we obtain new families of filiform Lie algebras of order 3, in which the complexity of the problem rises considerably respecting to the cases considered in Navarro (2014).