A (very short) introduction to buildings

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These lectures are an informal elementary introduction to buildings. They are written for, and by, a non-expert. The aim is to get to the definition of a building and feel that it is an entirely natural thing. To maintain the lecture style examples have replaced proofs. The notes at the end indicate where these proofs can be found.

The lectures are a distillation of the first few chapters of the books of Abramenko and Brown and of Ronan. Lecture 1 illustrates all the features of a building in the context of an example, but without mentioning any building terminology. In principle anyone could read this. Lectures 2-4 firm-up and generalize these specifics: Coxeter groups appear in Lecture 2, chambers systems in Lecture 3 and the definition of a building in Lecture 4. Lecture 5 addresses where buildings come from by describing the first important example: the spherical building of an algebraic group.
Original languageEnglish
Pages (from-to)221-247
Number of pages27
JournalExpositiones Mathematicae
Issue number3
Early online date1 Nov 2013
Publication statusPublished - 2014

Bibliographical note

(c) 2013 Elsevier. This is an author produced version of a paper published in Expositiones Mathematicae. Uploaded in accordance with the publisher's self-archiving policy.


  • Building
  • Coxeter group
  • Chamber system
  • Algebraic group

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