Three-point Lie algebras and Grothendieck's dessins d'enfants

2013/11/27 by Vladimir Chernousov, V. Chernousov, Philippe Gille +4
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1311.7097

16 pages

openalex publication_date 2013/11/27 · arxiv created 2015/01/07 · arxiv updated 2015/01/08 · openalex created_date 2019/07/30 · openalex updated_date 2026/07/28

Abstract

We define and classify the analogues of the affine Kac-Moody Lie algebras for the ring corresponding to the complex projective line minus three points. The classification is given in terms of Grothendieck's dessins d'enfants. We also study the question of conjugacy of Cartan subalgebras for these algebras.

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