  We introduce C-Algebras (quantum analogues of compact Riemann surfaces),
defined by polynomial relations in non-commutative variables and containing a
real parameter that, when taken to zero, provides a classical non-linear,
Poisson-bracket, obtainable from a single polynomial C(onstraint) function. For
a continuous class of quartic constraints, we explicitly work out finite
dimensional representations of the corresponding C-Algebras.
