Lectures on buildings / Mark Ronan ; Updated and Revised.

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Bibliographic Details
Main Author: Ronan, Mark
Language:English
Published: Chicago ; London : The University of Chicago Press, 2009.
Subjects:
Buildings (Group theory)
Finite geometries.
Finite groups.
Physical Description:xii, 228 pages
Format: Book
Contents:
  • Chamber systems and examples
  • Chamber systems
  • Two examples of buildings
  • Exercises
  • Coxeter complexes
  • Coxeter groups and complexes
  • Words and galleries
  • Reduced words and homotopy
  • Finite coxeter complexes
  • Self-homotopy
  • Exercises
  • Buildings
  • A definition of buildings
  • Generalised m-gons - the rank 2 case
  • Residues and apartments
  • Exercises
  • Local properties and coverings
  • Chamber systems of type m
  • Coverings and the fundamental group
  • The universal cover
  • Examples
  • Exercises
  • Bn - pairs
  • Tits systems and buildings
  • Parabolic subgroups
  • Exercises
  • Buildings of spherical type and root groups
  • Some basic lemmas
  • Root groups and the moufang property
  • Commutator relations
  • Moufang buildings - the general case
  • Exercises
  • A construction of buildings
  • Blueprints
  • Natural labellings of moufang buildings
  • Foundations
  • Exercises
  • The classification of spherical buildings
  • 1.a3 blueprints and foundations
  • Diagrams with single bonds
  • C3 foundations
  • Cn buildings for n > 4
  • Tits diagrams and f4 buildings
  • Finite buildings
  • Exercises
  • Affine buildings I
  • Affine coxeter complexes and sectors
  • The affine building an-1 (k,v)
  • The spherical building at infinity
  • The proof of (9.5)
  • Exercises
  • Affine buildings II
  • Apartment systems, trees and projective valuations
  • Trees associated to walls and panels at infinity
  • Root groups with a valuation
  • Construction of an affine bn-pair
  • The classification
  • An application
  • Exercises
  • Twin buildings
  • Twin buildings and kac-moody groups
  • Twin trees
  • Twin apartments
  • An example: affine twin buildings
  • Residues, rigidity, and proj
  • 2-spherical twin buildings
  • The moufang property and root group data
  • Twin trees again
  • Appendix 1: moufang polygons
  • The m-function
  • The natural labelling for a moufang plane
  • The non-existence theorem
  • Appendix 2: diagrams for moufang polygons
  • Appendix 3: non-discrete buildings
  • Appendix 4: topology and the steinberg representation
  • Appendix 5: finite coxeter groups
  • Appendix 6: finite buildings and groups of lie type.