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

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 $A_{\infty }$-cohomology, which we define in terms of the brace operations. As an example, we construct a minimal $A_{\infty }$-algebra from the Weyl–Moyal $\ast$-product algebra of polynomial functions.