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

## TL;DR

This paper introduces a method for constructing formal deformations of differential graded algebras using the Gerstenhaber algebra structure on $A_
abla$-cohomology, exemplified by the Weyl-Moyal algebra.

## Contribution

It presents a new approach to deforming $A_
abla$-algebras via Gerstenhaber algebra structures defined through brace operations.

## Key findings

- Constructed a minimal $A_
abla$-algebra from Weyl-Moyal $
abla$-product
- Defined Gerstenhaber algebra structure on $A_
abla$-cohomology
- Provided a simple method for formal deformations of differential graded algebras

## 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 from the Weyl-Moyal $\ast$-product algebra of polynomial functions.