Volume 14, issue 1 (2014)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Koszul duality theory for operads over Hopf algebras

Olivia Bellier

Algebraic & Geometric Topology 14 (2014) 1–35
Abstract

The transfer of the generating operations of an algebra to a homotopy equivalent chain complex produces higher operations. The first goal of this paper is to describe precisely the higher structure obtained when the unary operations commute with the contracting homotopy. To solve this problem, we develop the Koszul duality theory of operads in the category of modules over a cocommutative Hopf algebra. This gives rise to a simpler category of homotopy algebras and infinity morphisms, which allows us to get a new description of the homotopy category of algebras over such operads. The main example of this theory is given by Batalin–Vilkovisky algebras.

Keywords
operads, Batalin–Vilkovisky algebras, Koszul duality theory, homotopical algebra
Mathematical Subject Classification 2010
Primary: 18D50, 18G55
Secondary: 16W30, 55P48
References
Publication
Received: 25 February 2013
Revised: 6 June 2013
Accepted: 6 June 2013
Preview posted: 21 November 2013
Published: 9 January 2014
Authors
Olivia Bellier
Institut de Mathématiques de Toulouse
Université Paul Sabatier
118 route de Narbonne
31062 Toulouse Cedex 9
France
http://www.math.univ-toulouse.fr/~obellier