Contraction groups in complete Kac-Moody groups

Authors

Udo Baumgartner, The University of NewcastleFollow
Jacqueline Ramagge, University of WollongongFollow
Bertrand Remy, Université de LyonFollow

RIS ID

23854

Publication Details

Baumgartner, U., Ramagge, J. & Remy, B. (2008). Contraction groups in complete Kac-Moody groups. Groups, Geometry, and Dynamics, 2 (3), 337-352.

Abstract

Let G be an abstract Kac-Moody group over a finite field and overlineG the closure of the image of G in the automorphism group of its positive building. We show that if the Dynkin diagram associated to G is irreducible and neither of spherical nor of affine type, then the contraction groups of elements in overline G which are not topologically periodic are not closed. (In those groups there always exist elements which are not topologically periodic.)