  We consider an abstract Wick ordering as a family of relations on elements
a_i and define *-algebras by these relations. The relations are given by a
fixed operator T:h\otimes h --> h \otimes h, where h is one-particle space, and
they naturally define both a *-algebra and an inner-product space H_T, <.,.>_T.
If a_i^* denotes the adjoint, i.e., <a_i\phi,\psi>_T=<\phi,a_i^*\psi>_T, then
we identify when <.,.>_T is positive semidefinite (the positivity question). In
the case of deformations of the CCR-relations (the q_{ij}-CCR and the twisted
CCR's), we work out the universal C*-algebras A, and we prove that, in these
cases, the Fock representations of the A's are faithful.
