Geodesic
Koszul duality theory for operads over Hopf algebras
Bellier, Olivia1
1Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9, France
Algebraic and Geometric Topology, Tome 14 (2014) no. 1, pp. 1-35
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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.

DOI : 10.2140/agt.2014.14.1
Classification : 18D50, 18G55, 16W30, 55P48
Keywords: operads, Batalin–Vilkovisky algebras, Koszul duality theory, homotopical algebra

Bellier, Olivia  1

1 Institut de Mathématiques de Toulouse, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 9, France 
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Bellier, Olivia. Koszul duality theory for operads over Hopf algebras. Algebraic and Geometric Topology, Tome 14 (2014) no. 1, pp. 1-35. doi: 10.2140/agt.2014.14.1

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