2020, Ebrahimi-Fard, Kurusch, Patras, Frédéric, Tapia, Nikolas, Zambotti, Lorenzo

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.