Rational homotopy of Leibniz algebras

Abstract

We construct a non-commutative rational homotopy theory by replacing the pair (Lie algebras, commutative algebras) by the pair (Leibniz algebras, Leibniz-dual algebras). Both pairs are Koszul dual in the sense of operads (Ginzburg–Kapranov). We prove the existence of minimal models and the Hurewicz theorem in this framework. We define Leibniz spheres and prove that their homotopy is periodic.