Braided bialgebras of Hecke-type. (Q1014578)

The authors prove a version of the Milnor-Moore Theorem for connected braided bialgebras that are infinitesimally cocommutative. It is shown that over a field \(k\) of characteristic \(\neq 2\), a connected braided bialgebra \(A\) which is infinitesimally \(\lambda\)-cocommutative for some non-zero \(\lambda\in k\) which is not a root of unity, then the infinitesimal braiding of \(A\) is of Hecke type of mark \(\lambda\), and \(A\) is isomorphic as a braided bialgebra to the symmetric algebra of the braided subspace of its primitive elements.