  Heisenberg groups over algebras with central involution and their
automorphism groups are constructed. The complex quaternion group algebra over
a prime field is used as an example. Its subspaces provide finite models for
each of the real and complex quadratic spaces with dimension 4 or less. A model
for the representations of these Heisenberg groups and automorphism groups is
constructed. A pseudo-differential operator enables a parallel treatment of
spaces defined over finite and real fields.
