Contraction groups in complete Kac-Moody groups

Udo Baumgartner (1) , Jacqui Ramagge (2) , Bertrand Remy (3)

1 School of Mathematical and Physical Sciences
2 School of Mathematics and Applied Statistics [Wollongong]
3 ICJ - Institut Camille Jordan

Let $G$ be an abstract Kac-Moody group over a finite field and $\overline{G}$ be 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.)

Mots clés: contraction group; topological Kac-Moody group; totally disconnected; locally compact group

Domaines: Théorie des groupes [math.GR]

Udo Baumgartner, Jacqui Ramagge, Bertrand Remy. Contraction groups in complete Kac-Moody groups. 2007. ⟨hal-00155669⟩