English

Contraction groups in complete Kac-Moody groups

Group Theory 2012-10-04 v1

Abstract

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

Keywords

Cite

@article{arxiv.0706.2713,
  title  = {Contraction groups in complete Kac-Moody groups},
  author = {Udo Baumgartner and Jacqui Ramagge and Bertrand Remy},
  journal= {arXiv preprint arXiv:0706.2713},
  year   = {2012}
}
R2 v1 2026-06-21T08:39:43.837Z