  Motivated by questions in modular representation theory, Carlson,
Friedlander, and the first author introduced the varieties E(r, g) of
r-dimensional abelian p-nilpotent subalgebras of a p-restricted Lie algebra g.
In this paper, we identify the varieties E(r, g) for a reductive restricted Lie
algebra g and r the maximal dimension of an abelian p-nilpotent subalgebra of
g.
