Livernet, M., Roitzheim, C. and Whitehouse, S. orcid.org/0000-0002-7896-506X (2013) Derived A(infinity)-algebras in an operadic context. Algebraic and Geometric Topology, 13 (1). pp. 409-440. ISSN 1472-2739
Abstract
Derived A1–algebras were developed recently by Sagave. Their advantage over classical A1–algebras is that no projectivity assumptions are needed to study minimal models of differential graded algebras. We explain how derived A1–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 A1 as a resolution of the operad As encoding associative algebras. We further show that Sagave’s definition of morphisms agrees with the infinitymorphisms of dA1–algebras arising from operadic machinery. We also study the operadic homology of derived A1–algebras.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2013 Mathematical Sciences Publishers (MSP). This is an author produced version of a paper subsequently published in Algebraic and Geometric Topology. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 10 Jun 2016 13:54 |
Last Modified: | 24 Mar 2018 14:54 |
Published Version: | http://dx.doi.org/10.2140/agt.2013.13.409 |
Status: | Published |
Publisher: | Mathematical Sciences Publishers (MSP) |
Refereed: | Yes |
Identification Number: | 10.2140/agt.2013.13.409 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:100688 |