UNIQUENESS OF A∞-STRUCTURES AND HOCHSCHILD COHOMOLOGY

Abstract

Abstract. This paper investigates if a differential graded algebra can have more than one A∞structure extending the given differential graded algebra structure. We give a sufficient condition for uniqueness of such an A∞-structure up to quasi-isomorphism using Hochschild cohomology. We then extend this condition to Sagave’s notion of derived A∞-algebras after introducing a notion of Hochschild cohomology that applies to this.