Flat rank of automorphism groups of buildings

Title: Flat rank of automorphism groups of buildings
Creator: Baumgartner, Udo; Remy, Bertrand; Willis, George A.
Relation: Transformation Groups Vol. 12, Issue 3, p. 413-436
Publisher Link: http://dx.doi.org/10.1007/s00031-006-0050-3
Publisher: Birkhauser Boston
Resource Type: journal article
Date: 2007
Description: 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|) 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.
Subject: flat rank; automorphism groups; buildings
Identifier: uon:2417
Identifier: http://hdl.handle.net/1959.13/29145
Identifier: ISSN:1083-4362
Language: eng
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