Koszul duality theory for operads over Hopf algebras

Bellier, Olivia

doi:10.2140/agt.2014.14.1

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Koszul duality theory for operads over Hopf algebras

Olivia Bellier

Algebraic & Geometric Topology 14 (2014) 1–35

DOI: 10.2140/agt.2014.14.1

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

Volume 14, issue 1 (2014)