Mathematical Research Letters

Volume 23 (2016)

Number 1

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

Pages: 81 – 104



V. Chernousov (Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada)

P. Gille (UMR 5208 du CNRS, Institut Camille Jordan, Université Claude Bernard Lyon 1, Villeurbanne, France; and Institute of Mathematics Simion Stoilow of the Romanian Academy, Bucharest, Romania)

A. Pianzola (Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada; and Centro de Altos Estudios en Ciencia Exactas, Buenos Aires, Argentina)


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.


reductive group scheme, dessins d’enfants, torsor, loop algebra, affine and three-point affine Lie algebras, Cartan subalgebra

2010 Mathematics Subject Classification

11E72, 14E20, 14L30, 17B67

Published 25 May 2016