The Derived Deligne Conjecture

Abstract

Derived $A_{\infty }$-algebras have a wealth of theoretical advantages over regular $A_{\infty }$-algebras. However, due to their bigraded nature, in practice they are often unwieldy to work with. We develop a framework involving brace algebras on operads which allows us to study derived $A_{\infty }$ algebras in a new conceptual context. One particular advantage is that this construction allows us to generalize the Lie algebra structure on the Hochschild complex of an $A_{\infty }$-algebra, obtaining new and rigorous versions of the Deligne conjecture.

arXiv comment41 pages, comments welcome!