Homotopie rationnelle des algèbres de Leibniz

Abstract

Rational homotopy theory makes Lie algebras and commutative algebras dual to each other. In this Note, we extend this theory to the framework of Leibniz algebras. Leibniz dual algebras replace commutative algebras. We are thus able to define the homotopy and the homology of a Leibniz algebra. We state a Leibniz version of Hurewicz theorem. We define Leibniz spheres and prove that their homotopy is periodic.