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Transformation Groups

, Volume 12, Issue 3, pp 413–436 | Cite as

Flat rank of automorphism groups of buildings

  • Udo BaumgartnerEmail author
  • Bertrand RemyEmail author
  • George A. WillisEmail author
Article

Abstract

The flat rank of a totally disconnected locally compact group G, denoted flat-rk(G), is an invariant of the topological group structure of G. It is defined thanks to a natural distance on the space of compact open subgroups of G. For a topological Kac-Moody group G with Weyl group W, we derive the inequalities alg-rk(W) ≤ flat-rk(G) ≤ rk(|W|0). Here, alg-rk(W) is the maximal Z-rank of abelian subgroups of W, and rk(|W|0) is the maximal dimension of isometrically embedded flats in the CAT0-realization |W|0. We can prove these inequalities under weaker assumptions. We also show that for any integer n ≥ 1 there is a simple, compactly generated, locally compact, totally disconnected group G, with flat-rk(G) = n and which is not linear.

Keywords

Compact Group Weyl Group Coxeter Group Open Subgroup Compact Open Subgroup 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhauser Boston 2007

Authors and Affiliations

  1. 1.School of Mathematical and Physical Sciences, The University of Newcastle, University Drive, Building VCallaghan, NSW 2308Australia
  2. 2.Universite de Lyon, Lyon, F-69003, Universite de Lyon 1, Institut Camille Jordan, F-69622 and CNRS, UMR 5208Villeurbanne, F-69622France

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