Uniqueness of $A_\infty$–structures and Hochschild cohomology

Abstract

Working over a commutative ground ring, we establish a Hochschild cohomology criterion for uniqueness of derived $A_{\infty }$–algebra structures in the sense of Sagave. We deduce a Hochschild cohomology criterion for intrinsic formality of a differential graded algebra. This generalizes a classical result of Kadeishvili for the case of a graded algebra over a field.