Algèbres pré-Gerstenhaber à homotopie près

Abstract : This paper is concerned by the concept of algebra up to homotopy for a structure defined by two operations $.$ and $[~,~]$. An important example of such a structure is the Gerstenhaber algebra (commutatitve and Lie). The notion of Gerstenhaber algebra up to homotopy ($G_\infty$ algebra) is known. Here, we give a definition of pre-Gerstenhaber algebra (pre-commutative and pre-Lie) allowing the construction of $\hbox{pre}G_\infty$ algebra. Given a structure of pre-commutative (Zinbiel) and pre-Lie algebra and working over the corresponding dual operads, we will give an explicit construction of the associated pre-Gerstenhaber algebra up to homotopy, this is a bicogebra (Leibniz and permutative) equipped with a codifferential which is a coderivation for the two coproducts.
Mots-clés :
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

Cited literature [11 references]

https://hal.archives-ouvertes.fr/hal-00709757
Contributor : Didier Arnal <>
Submitted on : Tuesday, June 19, 2012 - 7:37:18 PM
Last modification on : Thursday, March 7, 2019 - 2:54:51 PM
Long-term archiving on : Thursday, September 20, 2012 - 2:30:32 AM

Files

pregersten.pdf
Files produced by the author(s)

Identifiers

• HAL Id : hal-00709757, version 1
• ARXIV : 1206.4335

Citation

Walid Aloulou, Didier Arnal, Ridha Chatbouri. Algèbres pré-Gerstenhaber à homotopie près. 2012. ⟨hal-00709757⟩

Record views