Geodesic
Homological perturbation theory and associativity
Homology, homotopy, and applications, Tome 2 (2000) no. 1, pp. 51-88.

Voir la notice de l'article provenant de la source International Press of Boston

In this paper, we prove various results concerning DGA-algebras in the context of the Homological Perturbation Theory. We distinguish two class of contractions for algebras: full algebra contractions and semi-full algebra contractions. A full algebra contraction is, in particular, a semi-full algebra contraction. Taking a full algebra contraction and an “algebra perturbation” as data of the Basic Perturbation Lemma, the Algebra Perturbation Lemma (or simply, F-APL) of [20] and [29] appears in a natural way. We establish here a perturbation machinery, the Semi-Full Algebra Perturbation Lemma (or, simply, SFAPL) that is a generalization of the previous one in the sense that the application range of SF-APL is wider than that of F-APL. We show four important applications in which this result is essential for the construction of algebra or coalgebra structures in various chain complexes.
DOI : 10.4310/HHA.2000.v2.n1.a5
Classification : 18G10, 18Gxx, 55U15, 55Uxx
Keywords: filtered algebra, graded algebra, resolutions, homological perturbation, differential homological algebra, augmented algebra, chain complex, contraction 
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Pedro Real. Homological perturbation theory and associativity. Homology, homotopy, and applications, Tome 2 (2000) no. 1, pp. 51-88. doi : 10.4310/HHA.2000.v2.n1.a5. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2000.v2.n1.a5/

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