On the Classification of Lie Bialgebras by Cohomological Means

2018/10/11 by Seidon Alsaody, Alsaody, Seidon, Arturo Pianzola +1
Mathematics · #17B37 #17B62 #20G10 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1810.05288

openalex publication_date 2018/10/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 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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