Three-point Lie algebras and Grothendieck’s dessins d’enfants. (English) Zbl 1406.17027
Summary: We define and classify the analogues of the affine Kac-Moody Lie algebras for the ring of functions on 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.
MSC:
17B65 | Infinite-dimensional Lie (super)algebras |
11E72 | Galois cohomology of linear algebraic groups |
14H57 | Dessins d’enfants theory |
14L30 | Group actions on varieties or schemes (quotients) |
20G10 | Cohomology theory for linear algebraic groups |
20G35 | Linear algebraic groups over adèles and other rings and schemes |