Belavin-Drinfeld quantum groups and Lie bialgebras: 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 $\mathbb{K}$ of characteristic 0 to the standard non-abelian Galois cohomology $H^1(\mathbb{K},\mathbf{H})$ for a suitable algebraic $\mathbb{K}$-group $\mathbf{H}.$ 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.

References in corpus (2)

• Classification of quantum groups and Belavin--Drinfeld cohomologies for orthogonal and symplectic Lie algebras
• Classification of quantum groups and Lie bialgebra structures on $sl(n,\mathbb{F})$. Relations with Brauer group