  Deformation theory of associative algebras and in particular of Poisson
algebras is reviewed. The role of an almost contraction leading to a canonical
solution of the corresponding Maurer-Cartan equation is noted. This role is
reminiscent of the homotopical perturbation lemma, with the infinitesimal
deformation cocycle as initiator.
  Applied to star-products, we show how Moyal's formula can be obtained using
such an almost contraction and conjecture that the merger operation provides a
canonical solution at least in the case of linear Poisson structures.
