Un theoreme de Milnor-Moore pour les algebres de Leibniz, by Francois Goichot

Leibniz algebras were introduced by J-L. Loday as "non-commutative" analogues of Lie algebras ; he also constructed the analogue of the enveloping algebra of a Lie algebra : the so-called enveloping dialgebra. In this framework, we show that the enveloping dialgebra of a Leibniz algebra has a natural "Hopf" structure. Then we prove a Milnor-Moore type theorem : the category of Leibniz algebras is equivalent to the category of irreducible cocommutative Hopf dialgebras. In the case of free objects, this gives analogues to the classical theorems of Friedrichs and Specht-Wever.


Francois Goichot <francois.goichot@univ-valenciennes.fr>