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arXiv · 1810.05288

On the Classification of Lie Bialgebras by Cohomological Means

Seidon Alsaody·Arturo Pianzola
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Abstract

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 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.

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BibTeXRIS

Seidon Alsaody, Arturo Pianzola. 2018-10-11. On the Classification of Lie Bialgebras by Cohomological Means. https://arxiv.org/abs/1810.05288

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