# Derived A-infinty algebras in an operadic context

Livernet, Muriel, Roitzheim, Constanze, Whitehouse, Sarah (2013) Derived A-infinty algebras in an operadic context. Algebraic & Geometric Topology, 13 (1). pp. 409-440. ISSN 1472-2739. (doi:10.2140/agt.2013.13.409)

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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, ie bicomplexes with an associative multiplication. This generalises the established result describing the operad A-infinity as a resolution of the operad As encoding associative algebras. We further show that 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.

Item Type: Article 10.2140/agt.2013.13.409 [UNSPECIFIED] Finiteness structures in chromatic derived categories Operads, A-infinity algebras, homological algebra Q Science > QA Mathematics (inc Computing science) > QA150 AlgebraQ Science > QA Mathematics (inc Computing science) > QA440 Geometry > QA611 Topology > QA612 Algebraic topology Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics Constanze Roitzheim 13 Mar 2013 09:28 UTC 29 May 2019 10:01 UTC https://kar.kent.ac.uk/id/eprint/33273 (The current URI for this page, for reference purposes)