The Cartier-Quillen-Milnor-Moore theorem in the Post-Hopf case

Abstract

We give the definition of left/right Post-Lie algebras and left/right Post-Hopf algebras and establish a link between those objects. We get a Cartier-Quillen-Milnor-Moore theorem for Post-Hopf algebras. We give another description for free Post-Lie algebras and a description for Post-Lie algebras obtained from an associative product.