2012/06/19 by Walid Aloulou, Aloulou, Walid, Didier Arnal +3
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1206.4335
openalex publication_date 2012/06/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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_∞ algebra) is known. Here, we give a definition of pre-Gerstenhaber algebra (pre-commutative and pre-Lie) allowing the construction of \hboxpreG_∞ 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.