  We construct C-algebras for a class of surfaces that are inverse images of
certain polynomials of arbitrary degree. By using the directed graph associated
to a matrix, the representation theory can be understood in terms of ``loop''
and ``string'' representations, which are closely related to the dynamics of an
iterated map in the plane. As a particular class of algebras we introduce the
``Henon algebras'', for which the dynamical map is a generalized Henon map, and
give an example where irreducible representations of all dimensions exist.
