2014/01/21 by Camil I. Aponte Román, Roman, Camil I. Aponte, Muriel Livernet +7
Mathematics · #18D50 16E45 18G55 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1401.5251
openalex publication_date 2014/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The notion of a derived A-infinity algebra arose in the work of Sagave as a natural generalisation of the classical A-infinity algebra, relevant to the case where one works over a commutative ring rather than a field. We develop some of the basic operadic theory of derived A-infinity algebras, building on work of Livernet-Roitzheim-Whitehouse. In particular, we study the coalgebras over the Koszul dual cooperad of the operad dAs, and provide a simple description of these. We study representations of derived A-infinity algebras and explain how these are a two-sided version of Sagave's modules over derived A-infinity algebras. We also give a new explicit example of a derived A-infinity algebra.