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Buildings

  • Chapter
Diagram Geometry

Abstract

The most important geometries of this book are of Coxeter type (cf. Definition 2.4.2). Their ‘building blocks’, that is, their rank two residues, are the generalized polygons (cf. Definition 2.2.7), which are precisely the rank two geometries of Coxeter type. In Chap. 4, we studied thin chamber systems of Coxeter type M and found that these are quotients of the very nice and regular universal chamber system \(\mathcal{C}(M)\) for Coxeter systems of type M. In this chapter, we study special chamber systems of Coxeter type, called buildings, in which \(\mathcal{C}(M)\) frequently occurs as a subsystem, which is called apartment.

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Authors and Affiliations

  1. Dépt. Mathématique, Université Libre de Bruxelles, Académie royale de Belgique, Bruxelles, Belgium

    Francis Buekenhout

  2. Dept. Mathematics & Computer Science, Eindhoven University of Technology, Eindhoven, Netherlands

    Arjeh M. Cohen

Authors
  1. Francis Buekenhout
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  2. Arjeh M. Cohen
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Buekenhout, F., Cohen, A.M. (2013). Buildings. In: Diagram Geometry. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics, vol 57. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34453-4_11

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