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We construct a solution of the master equation by means of standard toolsfrom homological perturbation theory under just the hypothesis that the groundfield be of characteristic zero, thereby avoiding the formality assumption ofthe relevant Lie algebra. To this end we endow the homology H(g) of anydifferential graded Lie algebra g with an sh-Lie structure such that g and H(g)are sh-equivalent. We discuss our solution of the master equation in thecontext of deformation theory. Given the extra structure appropriate to theextended moduli space of complex structures on a Calabi-Yau manifold, the knownsolutions result as a special case.

Formal solution of the master equation via HPT and deformation theory