DG-algebras and derived A-infinity algebras
Abstract
A differential graded algebra can be viewed as an A-infinity algebra. By a theorem of Kadeishvili, a dga over a field admits a quasi-isomorphism from a minimal A-infinity algebra. We introduce the notion of a derived A-infinity algebra and show that any dga A over an arbitrary commutative ground ring k is equivalent to a minimal derived A-infinity algebra. Such a minimal derived A-infinity algebra model for A is a k-projective resolution of the homology algebra of A together with a family of maps satisfying appropriate relations. As in the case of A-infinity algebras, it is possible to recover the dga up to quasi-isomorphism from a minimal derived A-infinity algebra model. Hence the structure we are describing provides a complete description of the quasi-isomorphism type of the dga.
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2007
- DOI:
- 10.48550/arXiv.0711.4499
- arXiv:
- arXiv:0711.4499
- Bibcode:
- 2007arXiv0711.4499S
- Keywords:
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- Mathematics - K-Theory and Homology;
- Mathematics - Algebraic Topology;
- Mathematics - Rings and Algebras;
- 16E45 (Primary);
- 16E40;
- 18G10;
- 18G55;
- 55S30 (Secondary)
- E-Print:
- v3: 27 pages. Minor corrections, to appear in Crelle's Journal