Lectures on buildings
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 -- G...
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Chicago u.a.
The Univ. of Chicago Press
2009
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| Ausgabe: | Updat. and rev. |
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| Online Zugang: | Inhaltstext |
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Tag hinzufügen | Zusammenfassung: | 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. |
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| Beschreibung: | Includes bibliographical references ([216]-221) and index |
| Beschreibung: | XII, 228 S graph. Darst 23cm |
| ISBN: | 0226724999 0-226-72499-9 9780226724997 978-0-226-72499-7 |