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

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Publisher
Springer International Publishing
Copyright
Copyright © 2016 by The Author(s)
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

References

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