English

Representations of derived A-infinity algebras

Algebraic Topology 2014-06-06 v2

Abstract

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.

Keywords

Cite

@article{arxiv.1401.5251,
  title  = {Representations of derived A-infinity algebras},
  author = {Camil I. Aponte Roman and Muriel Livernet and Marcy Robertson and Sarah Whitehouse and Stephanie Ziegenhagen},
  journal= {arXiv preprint arXiv:1401.5251},
  year   = {2014}
}

Comments

27 pages. To appear in the Proceedings of the August 2013 "Women in Topology" workshop at BIRS

R2 v1 2026-06-22T02:50:56.727Z