Flat rank of automorphism groups of buildings

dc.creatorBaumgartner, Udo
dc.creatorRemy, Bertrand
dc.creatorWillis, George A.
dc.date2005-10-14
dc.date2006-01-26
dc.date.accessioned2026-07-07T06:47:28Z
dc.date.available2026-07-07T06:47:28Z
dc.descriptionThe 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.identifierhttps://arxiv.org/abs/math/0510290
dc.identifierhttp://arxiv.org/abs/math/0510290
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/103664
dc.subjectGroup Theory
dc.subjectMetric Geometry
dc.subjectMSC2000: 22D05, 22D45
dc.titleFlat rank of automorphism groups of buildings
dc.typetext

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