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Walid Aloulou
Les $(a,b)$-algèbres à homotopie près
Annales mathématiques Blaise Pascal, 17 no. 1 (2010), p. 97-151, doi: 10.5802/ambp.279
Article PDF | Reviews MR 2674655 | Zbl 1204.18007
Class. Math.: 18G55, 16W30, 17B63, 16E45
Keywords: Algèbres homotopiques, cogèbres, algèbres de Poisson, algèbres différentielles graduées

Résumé - Abstract

We study in this article the concepts of algebra up to homotopy for a structure defined by two operations $ \hbox{.}$ and $[~,~]$. Having determined the structure of $ G_\infty $ algebras and $ P_\infty $ algebras, we generalize this construction and we define a structure of $ (a, b)$-algebra up to homotopy. Given a structure of commutative and differential graded Lie algebra for two shifts degree given by $a$ and $b$, we will give an explicit construction of the associate algebra up to homotopy and we clarify the relationship between $(a, b)$-algebra and algebra over the operad of little $n+1$-dimensional cubes.


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