Groups, Geometry, and Dynamics

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Volume 2, Issue 3, 2008, pp. 337–352
DOI: 10.4171/GGD/43

Published online: 2008-09-30

Contraction groups in complete Kac–Moody groups

Udo Baumgartner[1], Jacqui Ramagge[2] and Bertrand Rémy[3]

(1) University of Wollongong, Australia
(2) University of Sydney, Australia
(3) 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.)

Keywords: Contraction group, topological Kac–Moody group, totally disconnected, locally compact group

Baumgartner Udo, Ramagge Jacqui, Rémy Bertrand: Contraction groups in complete Kac–Moody groups. Groups Geom. Dyn. 2 (2008), 337-352. doi: 10.4171/GGD/43