Three-point Lie algebras and Grothendieck's dessins d'enfants
V. Chernousov, Philippe Gille (IMAR, ICJ), Arturo Pianzola

TL;DR
This paper introduces and classifies three-point Lie algebras related to the complex projective line minus three points, using Grothendieck's dessins d'enfants, and investigates their Cartan subalgebra conjugacy.
Contribution
It defines and classifies three-point Lie algebras via dessins d'enfants, extending the theory of affine Kac-Moody algebras to new geometric contexts.
Findings
Classification of three-point Lie algebras using dessins d'enfants
Analysis of conjugacy classes of Cartan subalgebras in these algebras
Connection between algebraic structures and geometric dessins
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Advanced Algebra and Geometry
