Belavin–Drinfeld solutions of the Yang–Baxter equation: Galois cohomology considerations

Abstract

We relate the Belavin–Drinfeld cohomologies (twisted and untwisted) that have been introduced in the literature to study certain families of quantum groups and Lie bialgebras over a non algebraically closed field K of characteristic 0 to the standard non-abelian Galois cohomology H1(K, H) for a suitable algebraic K-group H. 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.