Triangular braidings and pointed Hopf algebras

We consider an interesting class of braidings defined in [S. Ufer, PBW bases for a class of braided Hopf algebras, J. Algebra 280 (2004) 84–119] by a combinatorial property. We show that it consists exactly of those braidings that come from certain Yetter–Drinfeld module structures over pointed Hopf algebras with abelian coradical. As a tool we define a reduced version of the FRT construction. For braidings induced by image-modules the reduced FRT construction is calculated explicitly.