Contraction groups in complete Kac–Moody groups

  • Udo Baumgartner

    University of Wollongong, Australia
  • Jacqui Ramagge

    University of Sydney, Australia
  • Bertrand Rémy

    Université Claude Bernard Lyon 1, Villeurbanne, France


Let G be an abstract Kac–Moody group over a finite field and G 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 G which are not topologically periodic are not closed. (In such groups there always exist elements that are not topologically periodic.)

Cite this article

Udo Baumgartner, Jacqui Ramagge, Bertrand Rémy, Contraction groups in complete Kac–Moody groups. Groups Geom. Dyn. 2 (2008), no. 3, pp. 337–352

DOI 10.4171/GGD/43