Flat rank of automorphism groups of buildings

Baumgartner, Udo and Remy, Bertrand and Willis, George A. (2007) Flat rank of automorphism groups of buildings. Transformation Groups, 12 (3). pp. 413-436.

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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|â). Here, alg-rk(W) is the maximal Z-rank of abelian subgroups of W, and rk(|W|) is the maximal dimension of isometrically embedded flats in the CAT0-realization |W|â. 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.

Item Type: Article
Uncontrolled Keywords: flat rank, automorphism groups, buildings
Depositing User: Dr David Allingham
Date Deposited: 28 Sep 2012 12:05
Last Modified: 16 Oct 2013 16:52

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