PBW bases for a class of braided Hopf algebras

We prove the existence of a basis of Poincaré–Birkhoff–Witt type for braided Hopf algebras R generated by a braided subspace V P(R) if the braiding on V fulfills a triangularity condition. We apply our result to pointed Hopf algebras with abelian coradical and to Nichols algebras of low dimensional simple Uq(sl2)-modules.