  In this paper, we study moduli spaces of finite-dimensional Lie algebras with
flat center, proving that the forgetful map from Lie p-algebras to Lie algebras
is an affine fibration, and we point out a new case of existence of a
p-mapping. Then we illustrate these results for the special case of Lie
algebras of rank 3, whose moduli space we build and study over Z. We extend the
classical equivalence of categories between locally free Lie p-algebras of
finite rank with finite locally free group schemes of height 1, showing that
the centers of these objects correspond to each other. We finish by analysing
the smoothness of the moduli of p-Lie algebras of rank 3, in particular
identifying some smooth components.
