2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/75674Deformation 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.LaTeX, Elsevier style, 14 pages; submitted to Journal of Algebra 3/4/2005Quantum AlgebraMathematical Physics52Dxx; 58Hxxtext