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

V. Chernousov (1) , Philippe Gille (2, 3) , Arturo Pianzola (1)

1 University of Alberta
2 IMAR - "Simion Stoilow" Institute of Mathematics
3 AGL - Algèbre, géométrie, logique

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.

Mots clés: Cartan subalgebra; Reductive group scheme; multiloop algebra; affine and three pointed affine Lie algebras; Cartan subalgebra.; dessins d'enfants; torsor

Domaines: Anneaux et algèbres [math.RA]

V. Chernousov, Philippe Gille, Arturo Pianzola. Three-point Lie algebras and Grothendieck's dessins d'enfants. Mathematics Research Letters, 2016, 23, pp.81-104. ⟨hal-00910221v2⟩