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On axiomatic definitions of non-discrete affine buildings
-
C. D. Bennett
,
P. N. Schwer
Published/Copyright:
July 8, 2014
Abstract
We prove the equivalence of several sets of axioms for non-discrete affine buildings, by providing different types of metric, exchange and atlas conditions. We apply our result to show that the definition of a Euclidean building depends only on the topological equivalence class of the metric on the model space. The sharpness of the axioms dealing with metric conditions is illustrated in an appendix. There it is shown that a space X defined over a model space with metric d is possibly a building only if the induced distance function on X satisfies the triangle inequality.
Published Online: 2014-7-8
Published in Print: 2014-7-1
© 2014 by Walter de Gruyter Berlin/Boston
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Articles in the same Issue
- Masthead
- On axiomatic definitions of non-discrete affine buildings
- On Clifford analysis for holomorphic mappings
- Universal points of convex bodies and bisectors in Minkowski spaces
- The equal tangents property
- Some theorems of harmonic maps for Finsler manifolds
- The regular Grünbaum polyhedron of genus 5
- On the existence of nilsolitons on 2-step nilpotent Lie groups
- Rotational linear Weingarten hypersurfaces in the Euclidean sphere Sn+1
- Spacelike hypersurfaces in anti-de Sitter space
- The group of strong symplectic homeomorphisms in the L∞-metric
- The total Betti number of the intersection of three real quadrics
- On the algebraic models of symmetric smooth manifolds
- Non-existence of tight neighborly triangulated manifolds with β1 = 2
