Integrable deformations of nilpotent color Lie superalgebras

In this paper we study the infinitesimal deformations of the Z3Z3-color Lie superalgebra Ln,m,pLn,m,p. By means of these deformations all filiform Z3Z3-color Lie superalgebras can be obtained. In particular, we give a method that will allow us to determine the dimension of the subspaces that are composed by linearly integrable deformations.