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arXiv · 1110.5167

Derived A-infinity algebras in an operadic context

Muriel Livernet·Constanze Roitzheim·Sarah Whitehouse
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Abstract

Derived A-infinity algebras were developed recently by Sagave. Their advantage over classical A-infinity algebras is that no projectivity assumptions are needed to study minimal models of differential graded algebras. We explain how derived A-infinity algebras can be viewed as algebras over an operad. More specifically, we describe how this operad arises as a resolution of the operad dAs encoding bidgas. This generalises the established result describing the operad A-infinity as a resolution of the operad As encoding associative algebras. We further show Sagave's definition of morphisms agrees with the infinity-morphisms of dA-infinity algebras arising from operadic machinery. We also study the operadic homology of derived A-infinity algebras.

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Muriel Livernet, Constanze Roitzheim, Sarah Whitehouse. 2012-10-09. Derived A-infinity algebras in an operadic context. https://doi.org/10.2140/agt.2013.13.409

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