Diagram geometry : related to classical groups and buildings

F. Buekenhout, A.M. Cohen

Research output: Book/ReportBookAcademic

14 Citations (Scopus)

Abstract

This book provides a self-contained introduction to diagram geometry. Tight connections with group theory are shown. It treats thin geometries (related to Coxeter groups) and thick buildings from a diagrammatic perspective. Projective and affine geometry are main examples. Polar geometry is motivated by polarities on diagram geometries and the complete classification of those polar geometries whose projective planes are Desarguesian is given. It differs from Tits' comprehensive treatment in that it uses Veldkamp's embeddings. The book intends to be a basic reference for those who study diagram geometry. Group theorists will find examples of the use of diagram geometry. Light on matroid theory is shed from the point of view of geometry with linear diagrams. Those interested in Coxeter groups and those interested in buildings will find brief but self-contained introductions into these topics from the diagrammatic perspective. Graph theorists will find many highly regular graphs. The text is written so graduate students will be able to follow the arguments without needing recourse to further literature. A strong point of the book is the density of examples.
Original languageEnglish
Place of PublicationBerlin
PublisherSpringer
Number of pages592
ISBN (Electronic)9783642344534
ISBN (Print)978-3-642-34452-7
DOIs
Publication statusPublished - 2013

Publication series

NameErgebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge
Volume57
ISSN (Print)0071-1136

Fingerprint

Diagram Geometry
Classical Groups
Coxeter Group
Affine geometry
Projective geometry
Polarity
Group Theory
Projective plane
Matroid
Regular Graph
Diagram
Buildings
Graph in graph theory

Cite this

Buekenhout, F., & Cohen, A. M. (2013). Diagram geometry : related to classical groups and buildings. (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge; Vol. 57). Berlin: Springer. https://doi.org/10.1007/978-3-642-34453-4
Buekenhout, F. ; Cohen, A.M. / Diagram geometry : related to classical groups and buildings. Berlin : Springer, 2013. 592 p. (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge).
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Buekenhout, F & Cohen, AM 2013, Diagram geometry : related to classical groups and buildings. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, vol. 57, Springer, Berlin. https://doi.org/10.1007/978-3-642-34453-4

Diagram geometry : related to classical groups and buildings. / Buekenhout, F.; Cohen, A.M.

Berlin : Springer, 2013. 592 p. (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge; Vol. 57).

Research output: Book/ReportBookAcademic

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Buekenhout F, Cohen AM. Diagram geometry : related to classical groups and buildings. Berlin: Springer, 2013. 592 p. (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge). https://doi.org/10.1007/978-3-642-34453-4