We interpret in terms of non-abelian Galois cohomology the Belavin-Drinfeld cohomologies (twisted and untwisted) that have been introduced in the literature to study certain families of quantum groups and Lie bialgebras. The approach presented allows us to establish in full generality certain conjectures that were known to hold for the classical types of the split simple Lie algebras.

This is joint work with S. Alsaody and A. Stolin.