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arXiv · 2307.11414

The Derived Deligne Conjecture

Javier Aguilar Martín·Constanze Roitzheim
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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.

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Javier Aguilar Martín, Constanze Roitzheim. 2023-07-21. The Derived Deligne Conjecture. https://arxiv.org/abs/2307.11414

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