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We propose a simple method for constructing formal deformations ofdifferential graded algebras in the category of minimal $A_\infty$-algebras.The basis for our approach is provided by the Gerstenhaber algebra structure onthe $A_\infty$-cohomology, which we define in terms of the brace operations. Asan example, we construct a minimal $A_\infty$-algebra from the Weyl-Moyal$\ast$-product algebra of polynomial functions.

Cup product on $A_\infty$-cohomology and deformations