L ivernet, M., Roitzheim, C. and Whitehouse, S. (2013) Derived A-infinity algebras in an operadic context. Algebraic and Geometric Topology, 13, pp. 409-440. (doi: 10.2140/agt.2013.13.409)
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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 operadd As encoding bidgas, i.e. bicomplexes with an associative ultiplication. This generalises the established result describing the operad A1as a resolution of the operad As encoding associative algebras. We further show that Sagave’s definition of morphisms agrees with the infinity-morphisms of dA1-algebras arising from operadic machinery. We also study the operadic homology of derived A-infinity algebras.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Roitzheim, Dr Constanze |
| Authors: | L ivernet, M., Roitzheim, C., and Whitehouse, S. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics |
| Journal Name: | Algebraic and Geometric Topology |
| Publisher: | Mathematical Sciences Publishers |
| ISSN: | 1472-2747 |
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