  In this paper, we construct an example of a family of $4d$-dimensional
two-step nilpotent Lie algebras $(\frak g_d)_{d\geq 2}$ so that the cortex of
the dual of each $\frak g_d$ is a projective algebraic set. More precisely, we
show that the cortex of each dual $\frak g_d^*$ of $\frak g_d$ is the zero set
of a homogeneous polynomial of degree $d$. This example is a generalization of
one given in "Irreducible representations of locally compact groups that cannot
be Hausdorff separated from the identity representation" by "{\sc M.E.B. Bekka,
and E. Kaniuth}".
