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Euclidean Buildings: Geometry and Group Actions
 
Guy Rousseau Université de Lorraine, IECL, Vandoeuvre-lès-Nancy, France
A publication of European Mathematical Society
Hardcover ISBN:  978-3-98547-039-6
Product Code:  EMSTM/35
List Price: $109.00
AMS Member Price: $87.20
Please note AMS points can not be used for this product
Click above image for expanded view
Euclidean Buildings: Geometry and Group Actions
Guy Rousseau Université de Lorraine, IECL, Vandoeuvre-lès-Nancy, France
A publication of European Mathematical Society
Hardcover ISBN:  978-3-98547-039-6
Product Code:  EMSTM/35
List Price: $109.00
AMS Member Price: $87.20
Please note AMS points can not be used for this product
  • Book Details
     
     
    EMS Tracts in Mathematics
    Volume: 352023; 597 pp
    MSC: Primary 51; Secondary 20

    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. This 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).

    A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

    Readership

    Graduate students and research mathematicians interested in geometry, group theory, algebraic groups, and in the interactions between them.

  • Additional Material
     
     
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 352023; 597 pp
MSC: Primary 51; Secondary 20

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. This 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).

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and research mathematicians interested in geometry, group theory, algebraic groups, and in the interactions between them.

Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.