jump to search box

Diagram geometry : related to classical groups and buildings / Francis Buekenhout, Arjeh M. Cohen.

Availability

Online

At the Library

Other libraries

Author/Creator:
Buekenhout, Francis.
Language:
English.
Publication date:
2013
Imprint:
Berlin : Springer, c2013.
Format:
  • Book
  • xiii, 592 pages : illustrations ; 25 cm.
Title Variation:
Related to classical groups and buildings
Bibliography:
Includes bibliographical references and index.
Contents:
  • Geometries. The concept of a geometry ; Incidence systems and geometries ; Homomorphisms ; Subgeometries and truncations ; Residues ; Connectedness ; Permutation groups ; Groups and geometries ; Exercises ; Notes
  • Diagrams. The Digon diagram of a geometry ; Some parameters for rank two geometries ; Diagrams for higher rank geometries ; Coxeter diagrams ; Shadows ; Group diagrams ; A geometry of type Ãn-₁ ; Exercises ; Notes
  • Chamber systems. From a geometry to a chamber system ; Residues ; From chamber systems to geometries ; Connectedness ; The diagram of a chamber system ; Groups and chamber systems ; Exercises ; Notes
  • Thin geometries. Being Thin ; Thin geometries of coxeter type ; Groups generated by affine reflections ; Linear Reflection representations ; Root systems ; Finiteness criteria ; Finite coxeter groups ; Regulär polytopes revisited ; Exercises ; Notes
  • Linear geometries. The affine space of a Vector space ; The Projective space of a Vector space ; Matroids ; Matroids from geometries ; Steiner systems ; Geometries related to the golay code ; Exercises ; Notes
  • Projective and affine spaces. Perspectivities ; Projective lines ; Classification of projective spaces ; Classification of affine spaces ; Apartments ; Grassmannian geometry ; Root filtration spaces ; Exercises ; Notes
  • Polar spaces. Duality for geometries over a linear diagram ; Duality and sesquilinear forms ; Absolutes and reflexive sesquilinear forms ; Polar spaces ; The diagram of a polar space ; From diagram to space ; Singular subspaces ; Other shadow spaces of polar geometries ; Root filtration spaces ; Polar spaces with thin lines ; Exercises ; Notes
  • Projective embeddings of polar spaces. Geometric hyperplanes and ample connectedness ; The Veldkamp space ; Projective embedding for rank at least four ; Projective embedding for rank three ; Automorphisms of polar spaces ; Exercises ; Notes
  • Embedding polar spaces in absolutes. Embedded spaces ; Collars and tangent hyperplanes ; A Quasi-polarity ; Technical results on division rings ; Embedding in 3-dimensional space ; Exercises ; Notes
  • Classical polar spaces. Trace valued forms ; Pseudo-quadrics ; Perspective sets ; Apartments ; Automorphisms ; Finite classical polar spaces ; Exercises ; Notes
  • Buildings. Building axioms ; Properties of buildings ; Tits systems ; Shadow spaces ; Parapolar spaces ; Root shadow spaces ; Recognizing shadow spaces of buildings ; Exercises ; Notes
  • References
  • Index.
Contributor:
Cohen, Arjeh M.
Available in another form:
9783642344534 (online)
(GyWOH)har130101578
Series:
Ergebnisse der Mathematik und ihrer Grenzgebiete, 0071-1136 ; 3. Folge, volume 57
Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 57.
Subjects:
ISBN:
9783642344527
3642344526

powered by Blacklight
© Stanford University. Stanford, California 94305. (650) 725-1064. Terms of Use | Copyright Complaints | Opt Out of Analytics
jump to top