Geodesic
On the Classification of Lie Bialgebras by Cohomological Means
Documenta mathematica, Tome 24 (2019), pp. 2583-2612
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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 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.
DOI : 10.4171/dm/734
Classification : 17B37, 17B62, 20G10
Mots-clés : quantum group, Galois cohomology, Lie bialgebra, faithfully flat descent 
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     author = {Seidon Alsaody and Arturo Pianzola},
     title = {On the {Classification} of {Lie} {Bialgebras} by {Cohomological} {Means}},
     journal = {Documenta mathematica},
     pages = {2583--2612},
     year = {2019},
     volume = {24},
     doi = {10.4171/dm/734},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/734/}
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Seidon Alsaody; Arturo Pianzola. On the Classification of Lie Bialgebras by Cohomological Means. Documenta mathematica, Tome 24 (2019), pp. 2583-2612. doi: 10.4171/dm/734

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