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Abstract

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