Abstract
A differential graded algebra can be viewed as an A∞-algebra. By a theorem of Kadeishvili, a dga over a field admits a quasi-isomorphism from a minimal A∞-algebra. We introduce the notion of a derived A∞-algebra and show that any dga A over an arbitrary commutative ground ring k is equivalent to a minimal derived A∞-algebra. Such a minimal derived A∞-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∞-algebras, it is possible to recover the dga up to quasi-isomorphism from a minimal derived A∞-algebra model. Hence the structure we are describing provides a complete description of the quasi-isomorphism type of the dga.
© Walter de Gruyter Berlin · New York 2010
