A Milnor-Moore Type Theorem for Braided Bialgebras

Abstract

The paper is devoted to prove a version of Milnor-Moore Theorem for connected braided bialgebras that are infinitesimally cocommutative. Namely in characteristic different from 2, we prove that, for a given connected braided bialgebra $A$ having a $\hat{I}»$-cocommutative infinitesimal braiding for some regular element $\hat{I}»\ne 0$ in the base field, then the infinitesimal braiding of $A$ is of Hecke-type of mark $\hat{I}»$ and $A$ is isomorphic as a braided bialgebra to the symmetric algebra of the braided subspace of its primitive elements.