Livernet, Muriel, Roitzheim, Constanze, Whitehouse, Sarah (2013) Derived Ainfinty algebras in an operadic context. Algebraic & Geometric Topology, 13 (1). pp. 409440. ISSN 14722739. (doi:10.2140/agt.2013.13.409)
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Official URL http://dx.doi.org/10.2140/agt.2013.13.409 
Abstract
Derived Ainfinity algebras were developed recently by Sagave. Their advantage over classical Ainfinity algebras is that no projectivity assumptions are needed to study minimal models of differential graded algebras. We explain how derived Ainfinity 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 Ainfinity 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 dAinfinity –algebras arising from operadic machinery. We also study the operadic homology of derived Ainfinity algebras.
Item Type:  Article 

DOI/Identification number:  10.2140/agt.2013.13.409 
Projects:  [UNSPECIFIED] Finiteness structures in chromatic derived categories 
Uncontrolled keywords:  Operads, Ainfinity algebras, homological algebra 
Subjects: 
Q Science > QA Mathematics (inc Computing science) > QA150 Algebra Q Science > QA Mathematics (inc Computing science) > QA440 Geometry > QA611 Topology > QA612 Algebraic topology 
Divisions:  Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Pure Mathematics 
Depositing User:  Constanze Roitzheim 
Date Deposited:  13 Mar 2013 09:28 UTC 
Last Modified:  29 May 2019 10:01 UTC 
Resource URI:  https://kar.kent.ac.uk/id/eprint/33273 (The current URI for this page, for reference purposes) 
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