  Wick polynomials and Wick products are studied in the context of
non-commutative probability theory. It is shown that free, boolean and
conditionally free Wick polynomials can be defined and related through the
action of the group of characters over a particular Hopf algebra. These results
generalize our previous developments of a Hopf algebraic approach to cumulants
and Wick products in classical probability theory.
