Les (a,b)-algèbres à homotopie près

Walid Aloulou (1, 2)

1 Département de Mathématiques, Unité de recherche Physique Mathématique
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]

We study in this article the concepts of algebra up to homotopy for a structure defined by two operations $ \pt $ 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

Mots clés: Algèbres homotopiques; cogèbres; algèbres de Poisson; algèbres différentielles graduées

Domaines: Algèbres quantiques [math.QA]

Walid Aloulou. Les (a,b)-algèbres à homotopie près. 2008. ⟨hal-00295013⟩