Geodesic
On the Classification of Lie Bialgebras by Cohomological Means
Documenta mathematica, Tome 24 (2019), pp. 2583-2612.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We approach the classification of Lie bialgebra structures on simple Lie algebras from the viewpoint of descent and non-abelian cohomology. We achieve a description of the problem in terms of faithfully flat cohomology over an arbitrary ring over $\mathbb{Q}$, and solve it for Drinfeld-Jimbo Lie bialgebras over fields of characteristic zero. We consider the classification up to isomorphism, as opposed to equivalence, and treat split and non-split Lie algebras alike. We moreover give a new interpretation of scalar multiples of Lie bialgebras hitherto studied using twisted Belavin-Drinfeld cohomology.
Classification : 17B62, 17B37, 20G10
Keywords: Lie bialgebra, quantum group, faithfully flat descent, Galois cohomology 
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     author = {Alsaody, Seidon and Pianzola, Arturo},
     title = {On the {Classification} of {Lie} {Bialgebras} by {Cohomological} {Means}},
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Alsaody, Seidon; Pianzola, Arturo. On the Classification of Lie Bialgebras by Cohomological Means. Documenta mathematica, Tome 24 (2019), pp. 2583-2612. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a1/