Representations of derived Ainfinity algebras
Abstract
The notion of a derived Ainfinity algebra arose in the work of Sagave as a natural generalisation of the classical Ainfinity 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 Ainfinity algebras, building on work of LivernetRoitzheimWhitehouse. 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 Ainfinity algebras and explain how these are a twosided version of Sagave's modules over derived Ainfinity algebras. We also give a new explicit example of a derived Ainfinity algebra.
 Publication:

arXiv eprints
 Pub Date:
 January 2014
 arXiv:
 arXiv:1401.5251
 Bibcode:
 2014arXiv1401.5251A
 Keywords:

 Mathematics  Algebraic Topology;
 18D50 16E45 18G55
 EPrint:
 27 pages. To appear in the Proceedings of the August 2013 "Women in Topology" workshop at BIRS