WIAS Preprint No. 2677, (2020)

Wick polynomials in non-commutative probability: A group-theoretical approach


  • Ebrahimi-Fard, Kurusch
  • Patras, Frédéric
  • Tapia, Nikolas
    ORCID: 0000-0003-0018-2492
  • Zambotti, Lorenzo

2010 Mathematics Subject Classification

  • 16T05 16T10 16T30


  • Wick polynomials, monotone cumulants, free cumulants, boolean cumulants, formal power series, combinatorial Hopf algebra, shuffle algebra, group actions




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.

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