Simplicity of twin tree lattices with non-trivial commutation relations

Pierre-Emmanuel Caprace (1) , Bertrand Remy (2)

1 Département de mathématique [Louvain]
2 ICJ - Institut Camille Jordan

We prove a simplicity criterion for certain twin tree lattices. It applies to all rank two Kac-Moody groups over finite fields with non-trivial commutation relations, thereby yielding examples of simple non-uniform lattices in the product of two trees.

Mots clés: Kac-Moody group; twin tree; simplicity; residual finiteness; root system; building

Domaines: Théorie des groupes [math.GR]

Pierre-Emmanuel Caprace, Bertrand Remy. Simplicity of twin tree lattices with non-trivial commutation relations. 2012. ⟨hal-00734731⟩