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

Belavin–Drinfeld solutions of the Yang–Baxter equation: Galois cohomology considerations 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 $$\mathbb {K}$$ K of characteristic 0 to the standard non-abelian Galois cohomology $$H^1(\mathbb {K}, \mathbf{H})$$ H 1 ( K , H ) for a suitable algebraic $$\mathbb {K}$$ K -group $$\mathbf{H}.$$ 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Bulletin of Mathematical Sciences Springer Journals

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

, Volume 8 (1) – Dec 9, 2016
14 pages

/lp/springer_journal/belavin-drinfeld-solutions-of-the-yang-baxter-equation-galois-Pkmc3qWiWi
Publisher
Springer Journals
Subject
Mathematics; Mathematics, general
ISSN
1664-3607
eISSN
1664-3615
D.O.I.
10.1007/s13373-016-0094-1
Publisher site
See Article on Publisher Site

### 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 $$\mathbb {K}$$ K of characteristic 0 to the standard non-abelian Galois cohomology $$H^1(\mathbb {K}, \mathbf{H})$$ H 1 ( K , H ) for a suitable algebraic $$\mathbb {K}$$ K -group $$\mathbf{H}.$$ 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.

### Journal

Bulletin of Mathematical SciencesSpringer Journals

Published: Dec 9, 2016

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