  Manifestly consistent Fock representations of non-central (but
``core-central'') extensions of the $Z^N$-graded algebras of functions and
vector fields on the $N$-dimensional torus $T^N$ are constructed by a kind of
renormalization procedure. These modules are of lowest-energy type, but the
energy is not a linear function of the momentum. Modulo a technical assumption,
reducibility conditions are proved for the extension of $vect(T^N)$, analogous
to the discrete series of Virasoro representations.
