Braided bialgebras of Hecke-type

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,cA) which is infinitesimally λ-cocommutative for some element λ≠0 that is not a root of one in the base field, then the infinitesimal braiding of A is of Hecke-type of mark λ and A is isomorphic as a braided bialgebra to the symmetric algebra of the braided subspace of its primitive elements.