Cirici, J., Egas Santander, D., Livernet, M. et al. (1 more author) (2018) Derived A-infinity algebras and their homotopies. Topology and its Applications, 235. pp. 214-268. ISSN 0166-8641
Abstract
The notion of a derived A-infinity algebra, considered by Sagave, is a generalization of the classical notion of A-infinity algebra, relevant to the case where one works over a commutative ring rather than a field. We initiate a study of the homotopy theory of these algebras, by introducing a hierarchy of notions of homotopy between the morphisms of such algebras. We define r-homotopy, for non-negative integers r, in such a way that r-homotopy equivalences underlie Er-quasi-isomorphisms, defined via an associated spectral sequence. We study the special case of twisted complexes (also known as multicomplexes) first since it is of independent interest and this simpler case clearly exemplifies the structure we study. We also give two new interpretations of derived A-infinity algebras as A-infinity algebras in twisted complexes and as A-infinity algebras in split filtered cochain complexes.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Elsevier. This is an author produced version of a paper subsequently published in Topology and its Applications. Uploaded in accordance with the publisher's self-archiving policy. Article available under the terms of the CC-BY-NC-ND licence (https://creativecommons.org/licenses/by-nc-nd/4.0/) |
Keywords: | Derived A-infinity algebra; Filtered A-infinity algebra; Twisted complex; Multicomplex |
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: | 11 Jul 2017 08:52 |
Last Modified: | 06 Dec 2018 01:38 |
Published Version: | https://doi.org/10.1016/j.topol.2017.12.004 |
Status: | Published |
Publisher: | Elsevier |
Refereed: | Yes |
Identification Number: | 10.1016/j.topol.2017.12.004 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:118636 |
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