On some pro-p groups from infinite-dimensional Lie theory

Inna Capdeboscq (1) , Bertrand Remy (2)

1 WMI - Warwick Mathematics Institute
2 ICJ - Institut Camille Jordan

We initiate the study of some pro-p-groups arising from infinite-dimensional Lie theory. These groups are completions of some subgroups of incomplete Kac-Moody groups over finite fields, with respect to various completions of algebraic or geometric origin. We show topological finite generation for the pro-p Sylow subgroups in many complete Kac-Moody groups. This implies abstract simplicity of the latter groups. We also discuss with the question of (non-)linearity of these pro-p groups.

Mots clés: Kac-Moody theory; infinite root systems; pro-p groups; abstract simplicity; rigidity; non-linearity

Domaines: Théorie des groupes [math.GR]

Inna Capdeboscq, Bertrand Remy. On some pro-p groups from infinite-dimensional Lie theory. 2013. ⟨hal-00789284⟩