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) (KAR id:33273)
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Official URL: http://dx.doi.org/10.2140/agt.2013.13.409 |
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 |
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DOI/Identification number: | 10.2140/agt.2013.13.409 |
Projects: | Finiteness structures in chromatic derived categories |
Uncontrolled keywords: | Operads, A-infinity 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: | Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science |
Funders: | Organisations -1 not found. |
Depositing User: | Constanze Roitzheim |
Date Deposited: | 13 Mar 2013 09:28 UTC |
Last Modified: | 10 Dec 2022 00:34 UTC |
Resource URI: | https://kar.kent.ac.uk/id/eprint/33273 (The current URI for this page, for reference purposes) |
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