Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.13/29145
- Title
- Flat rank of automorphism groups of buildings
- Author/Creator
-
Baumgartner, Udo;
Remy, Bertrand;
Willis, George A.
- 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.
- Relation
- Transformation Groups Vol. 12, Issue 3, p. 413-436
- Publisher Link
- http://dx.doi.org/10.1007/s00031-006-0050-3
- Date
- 2007
- Publisher
- Birkhauser Boston
- Keyword(s)
-
flat rank;
automorphism groups;
buildings
- Resource Type
- journal article
- Identifier
- http://hdl.handle.net/1959.13/29145
- Identifier
- ISSN:1083-4362
- Language
- eng
- Reviewed
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