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Euclidean Buildings | Geometry and Group Actions

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Title: Euclidean Buildings | Geometry and Group Actions
Description: The theory of buildings lies at the interplay between geometry and group theory, and is one of the main tools for studying the structure of many groups. Actually, buildings were introduced by Jacques Tits in the 1950s to better understand and study a semi-simple algebraic group over a field. For a general field, its associated building is a spherical building, called its Tits building. It is a simplicial complex and, in this book, one considers a geometric realization called vectorial building. When the field is real valued, François Bruhat and Jacques Tits constructed another building taking into account the topology of the field. This Bruhat–Tits building is a polysimplicial complex and its usual geometric realization is an affine building. These vectorial or affine buildings are the main examples of Euclidean buildings. The present book develops the general abstract theory of these Euclidean buildings (the buildings with Euclidean affine spaces as apartments). It is largely self-contained and emphasizes the metric aspects of these objects, as CAT(0) spaces very similar to Riemannian symmetric spaces of non-compact type. The book studies their compactifications, their links with groups, many classical examples, and some applications (for example, to Hecke algebras).
Authors: Guy Rousseau
Resource Type: eBook.
Subjects: Buildings (Group theory), Geometric group theory
Categories: MATHEMATICS / Geometry / General, MATHEMATICS / Group Theory
Database: eBook Collection (EBSCOhost)
FullText Links:
  – Type: ebook-pdf
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  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 3808238
RelevancyScore: 1116
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
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  Data: Euclidean Buildings | Geometry and Group Actions
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  Data: The theory of buildings lies at the interplay between geometry and group theory, and is one of the main tools for studying the structure of many groups. Actually, buildings were introduced by Jacques Tits in the 1950s to better understand and study a semi-simple algebraic group over a field. For a general field, its associated building is a spherical building, called its Tits building. It is a simplicial complex and, in this book, one considers a geometric realization called vectorial building. When the field is real valued, François Bruhat and Jacques Tits constructed another building taking into account the topology of the field. This Bruhat–Tits building is a polysimplicial complex and its usual geometric realization is an affine building. These vectorial or affine buildings are the main examples of Euclidean buildings. The present book develops the general abstract theory of these Euclidean buildings (the buildings with Euclidean affine spaces as apartments). It is largely self-contained and emphasizes the metric aspects of these objects, as CAT(0) spaces very similar to Riemannian symmetric spaces of non-compact type. The book studies their compactifications, their links with groups, many classical examples, and some applications (for example, to Hecke algebras).
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  Data: <searchLink fieldCode="DE" term="%22Buildings+%28Group+theory%29%22">Buildings (Group theory)</searchLink><br /><searchLink fieldCode="DE" term="%22Geometric+group+theory%22">Geometric group theory</searchLink>
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RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 512.2
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Buildings (Group theory)
        Type: general
      – SubjectFull: Geometric group theory
        Type: general
    Titles:
      – TitleFull: Euclidean Buildings | Geometry and Group Actions
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Guy Rousseau
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            NameFull: Guy Rousseau
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          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2023
            – D: 23
              M: 03
              Type: profile
              Y: 2024
          Identifiers:
            – Type: isbn-print
              Value: 9783985470396
            – Type: isbn-electronic
              Value: 9783985475391
          Numbering:
            – Type: volume
              Value: 00035
          Titles:
            – TitleFull: Euclidean Buildings | Geometry and Group Actions
              Type: main
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