Wick Order, Spreadability and Exchangeability for Monotone Commutation Relations

We exhibit a Hamel basis for the concrete * -algebra M associated to monotone commutation relations realised on the monotone Fock space, mainly composed by Wick ordered words of annihilators and creators. We apply such a result to investigate spreadability and exchangeability of the stochastic processes arising from such commutation relations. In particular, we show that spreadability comes from a monoidal action implementing a dissipative dynamics on the norm closure C-algebra M= M¯. Finally, we determine the structure of the set of exchangeable and spreadable monotone stochastic processes, by showing that both coincide with the stationary ones.