Flat rank of automorphism groups of buildings
| dc.creator | Baumgartner, Udo | |
| dc.creator | Remy, Bertrand | |
| dc.creator | Willis, George A. | |
| dc.date | 2005-10-14 | |
| dc.date | 2006-01-26 | |
| dc.date.accessioned | 2026-07-07T06:47:28Z | |
| dc.date.available | 2026-07-07T06:47:28Z | |
| dc.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)\le flat-rk(G)\le rk(|W|\_0). Here, alg-rk(W) is the maximal $\mathbb{Z}$-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 \geq 1 there is a topologically simple, compactly generated, locally compact, totally disconnected group G, with flat-rk(G)=n and which is not linear. | |
| dc.identifier | https://arxiv.org/abs/math/0510290 | |
| dc.identifier | http://arxiv.org/abs/math/0510290 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/103664 | |
| dc.subject | Group Theory | |
| dc.subject | Metric Geometry | |
| dc.subject | MSC2000: 22D05, 22D45 | |
| dc.title | Flat rank of automorphism groups of buildings | |
| dc.type | text |