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El. knyga: Structure of Affine Buildings

  • Formatas: 384 pages
  • Serija: Annals of Mathematics Studies
  • Išleidimo metai: 08-Sep-2008
  • Leidėjas: Princeton University Press
  • Kalba: eng
  • ISBN-13: 9781400829057
  • Formatas: 384 pages
  • Serija: Annals of Mathematics Studies
  • Išleidimo metai: 08-Sep-2008
  • Leidėjas: Princeton University Press
  • Kalba: eng
  • ISBN-13: 9781400829057

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Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions and residues of these buildings.

In The Structure of Affine Buildings, Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions, and residues of these buildings. It also includes tables correlating the results in the locally finite case with the results of Tits's classification of absolutely simple algebraic groups defined over a local field. A companion to Weiss's The Structure of Spherical Buildings, The Structure of Affine Buildings is organized around the classification of spherical buildings and their root data as it is carried out in Tits and Weiss's Moufang Polygons.
Preface vii
Affine Coxeter Diagrams
1(12)
Root Systems
13(12)
Root Data with Valuation
25(14)
Sectors
39(6)
Faces
45(8)
Gems
53(6)
Affine Buildings
59(8)
The Building at Infinity
67(10)
Trees with Valuation
77(12)
Wall Trees
89(12)
Panel Trees
101(6)
Tree-Preserving Isomorphisms
107(12)
The Moufang Property at Infinity
119(12)
Existence
131(16)
Partial Valuations
147(12)
Bruhat-Tits Theory
159(8)
Completions
167(8)
Automorphisms and Residues
175(14)
Quadrangles of Quadratic Form Type
189(16)
Quadrangles of Indifferent Type
205(4)
Quadrangles of Type E6, E7, and E8
209(12)
Quadrangles of Type F4
221(8)
Quadrangles of Involutory Type
229(10)
Pseudo-Quadratic Quadrangles
239(22)
Hexagons
261(14)
Assorted Conclusions
275(14)
Summary of the Classification
289(8)
Locally Finite Bruhat-Tits Buildings
297(24)
Appendix A 321(22)
Appendix B 343(18)
Bibliography 361(4)
Index 365
Richard M. Weiss is the William Walker Professor of Mathematics at Tufts University and Honorary Professor in the School of Mathematics and Statistics at the University of Birmingham in the United Kingdom. He is the author of "The Structure of Spherical Buildings" and "Quadrangular Algebras" (both Princeton) and the coauthor with Jacques Tits of "Moufang Polygons". He received a Humboldt Research Prize in 2004.