Uniqueness of $A_{\infty }$-structures and Hochschild cohomology

Abstract

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

The paper has been rearranged and the results are now formulated in terms of a filtration of the Hochschild cohomology groups. To appear in Algebraic and Geometric Topology

References in corpus (2)

• A curious example of two model categories and some associated differential graded algebras
• DG-algebras and derived A-infinity algebras

Cited by in corpus (4)

• Formality of $\mathbb{P}$-objects
• Derived A-infinity algebras in an operadic context
• Tilting objects in periodic triangulated categories
• $A_{\infty }$-deformations of zigzag algebras via Ginzburg dg algebras