Lectures on buildings
By: Mark Ronan ; with a new introduction.
Publisher: The University of Chicago Press
Published: 2009
Place of publication: Chicago; London
Language: eng
Number of pages: 228
ISBN-13: 9780226724997
Subjects: Buildings (Group theory); Finite geometries; Finite groups
Notes: Includes bibliographical references and index.
Table of contents: title: Chamber systems and examples; title: Chamber systems; title: Two examples of buildings; title: Exercises; title: Coxeter complexes; title: Coxeter groups and complexes; title: Words and galleries; title: Reduced words and homotopy; title: Finite coxeter complexes; title: Self-homotopy; title: Exercises; title: Buildings; title: A definition of buildings; title: Generalised m-gons - the rank 2 case; title: Residues and apartments; title: Exercises; title: Local properties and coverings; title: Chamber systems of type m; title: Coverings and the fundamental group; title: The universal cover; title: Examples; title: Exercises; title: Bn - pairs; title: Tits systems and buildings; title: Parabolic subgroups; title: Exercises; title: Buildings of spherical type and root groups; title: Some basic lemmas; title: Root groups and the moufang property; title: Commutator relations; title: Moufang buildings - the general case; title: Exercises; title: A construction of buildings; title: Blueprints; title: Natural labellings of moufang buildings; title: Foundations; title: Exercises; title: The classification of spherical buildings; title: 1.a3 blueprints and foundations; title: Diagrams with single bonds; title: C3 foundations; title: Cn buildings for n > 4; title: Tits diagrams and f4 buildings; title: Finite buildings; title: Exercises; title: Affine buildings I; title: Affine coxeter complexes and sectors; title: The affine building an-1 (k,v); title: The spherical building at infinity; title: The proof of (9.5); title: Exercises; title: Affine buildings II; title: Apartment systems, trees and projective valuations; title: Trees associated to walls and panels at infinity; title: Root groups with a valuation; title: Construction of an affine bn-pair; title: The classification; title: An application; title: Exercises; title: Twin buildings; title: Twin buildings and kac-moody groups; title: Twin trees; title: Twin apartments; title: An example: affine twin buildings; title: Residues, rigidity, and proj; title: 2-spherical twin buildings; title: The moufang property and root group data; title: Twin trees again; title: Appendix 1: moufang polygons; title: The m-function; title: The natural labelling for a moufang plane; title: The non-existence theorem; title: Appendix 2: diagrams for moufang polygons; title: Appendix 3: non-discrete buildings; title: Appendix 4: topology and the steinberg representation; title: Appendix 5: finite coxeter groups; title: Appendix 6: finite buildings and groups of lie type.