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2013 Derived $A_{\infty}$–algebras in an operadic context
Muriel Livernet, Constanze Roitzheim, Sarah Whitehouse
Algebr. Geom. Topol. 13(1): 409-440 (2013). DOI: 10.2140/agt.2013.13.409


Derived A–algebras were developed recently by Sagave. Their advantage over classical A–algebras is that no projectivity assumptions are needed to study minimal models of differential graded algebras. We explain how derived A–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 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–algebras arising from operadic machinery. We also study the operadic homology of derived A–algebras.


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Muriel Livernet. Constanze Roitzheim. Sarah Whitehouse. "Derived $A_{\infty}$–algebras in an operadic context." Algebr. Geom. Topol. 13 (1) 409 - 440, 2013.


Received: 8 June 2012; Revised: 10 September 2012; Accepted: 4 October 2012; Published: 2013
First available in Project Euclid: 19 December 2017

zbMATH: 1268.18006
MathSciNet: MR3031646
Digital Object Identifier: 10.2140/agt.2013.13.409

Primary: 16E45, 18D50
Secondary: 18G10, 18G55

Rights: Copyright © 2013 Mathematical Sciences Publishers


Vol.13 • No. 1 • 2013
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