- Title Pages
- Dedication
- Epigraph
- Preface
-
Chapter One Buildings -
Chapter Two Quadratic Forms -
Chapter Three Moufang Polygons -
Chapter Four Moufang Quadrangles -
Chapter Five Linked Tori, I -
Chapter Six Linked Tori, II -
Chapter Seven Quadratic Forms over a ∈ Local Field -
Chapter Eight Quadratic Forms of Type E6, E7 and E8 -
Chapter Nine Quadratic Forms of Type F4 -
Chapter Ten Residues -
Chapter Eleven Unramified Quadrangles of Type E6, E7 and E8 -
Chapter Twelve Semi-ramified Quadrangles of Type E6, E7 and E8 -
Chapter Thirteen Ramified Quadrangles of Type E6, E7 and E8 -
Chapter Fourteen Quadrangles of Type E6, E7 and E8: Summary -
Chapter Fifteen Totally Wild Quadratic Forms of Type E7 -
Chapter Sixteen Existence -
Chapter Seventeen Quadrangles of Type F4 -
Chapter Eighteen The Other Bruhat-Tits Buildings -
Chapter Nineteen Coxeter Groups -
Chapter Twenty Tits Indices -
Chapter Twenty One Parallel Residues -
Chapter Twenty Two Fixed Point Buildings -
Chapter Twenty Three Subbuildings -
Chapter Twenty Four Moufang Structures -
Chapter Twenty Five Fixed Apartments -
Chapter Twenty Six The Standard Metric -
Chapter Twenty Seven Affine Fixed Point Buildings -
Chapter Twenty Eight Pseudo-Split Buildings -
Chapter Twenty Nine Linear Automorphisms -
Chapter Thirty Strictly Semi-linear Automorphisms -
Chapter Thirty One Galois Involutions -
Chapter Thirty Two Unramified Galois Involutions -
Chapter Thirty Three Residually Pseudo-Split Buildings -
Chapter Thirty Four Forms of Residually Pseudo-Split Buildings -
Chapter Thirty Five Orthogonal Buildings -
Chapter Thirty Six Indices for the Exceptional Bruhat-Tits Buildings - Bibliography
- Index
Orthogonal Buildings
Orthogonal Buildings
- Chapter:
- (p.303) Chapter Thirty Five Orthogonal Buildings
- Source:
- Descent in Buildings (AM-190)
- Author(s):
Bernhard M¨uhlherr
Holger P. Petersson
Richard M. Weiss
- Publisher:
- Princeton University Press
This chapter presents a few results about certain forms of orthogonal buildings. It begins with notations stating that V is a K-vector space of positive dimension, (K, V, q) is a quadratic space of positive dimension, (K, V, q) is a regular quadratic space of positive Witt index, S is the vertex set of the Coxeter diagram, (K, V, q) is a hyperbolic quadratic space of dimension 2n for some n greater than or equal to 3, S is the vertex set of the Coxeter diagram for some n greater than or equal to 3, and Dn.l,script small l is the Tits index of absolute type Dn for n greater than or equal to 3. The chapter also considers propositions dealing with regular quadratic spaces and hyperbolic quadratic spaces.
Keywords: orthogonal building, quadratic space, Witt index, vertex, Coxeter diagram, hyperbolic quadratic space, Tits index
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- Title Pages
- Dedication
- Epigraph
- Preface
-
Chapter One Buildings -
Chapter Two Quadratic Forms -
Chapter Three Moufang Polygons -
Chapter Four Moufang Quadrangles -
Chapter Five Linked Tori, I -
Chapter Six Linked Tori, II -
Chapter Seven Quadratic Forms over a ∈ Local Field -
Chapter Eight Quadratic Forms of Type E6, E7 and E8 -
Chapter Nine Quadratic Forms of Type F4 -
Chapter Ten Residues -
Chapter Eleven Unramified Quadrangles of Type E6, E7 and E8 -
Chapter Twelve Semi-ramified Quadrangles of Type E6, E7 and E8 -
Chapter Thirteen Ramified Quadrangles of Type E6, E7 and E8 -
Chapter Fourteen Quadrangles of Type E6, E7 and E8: Summary -
Chapter Fifteen Totally Wild Quadratic Forms of Type E7 -
Chapter Sixteen Existence -
Chapter Seventeen Quadrangles of Type F4 -
Chapter Eighteen The Other Bruhat-Tits Buildings -
Chapter Nineteen Coxeter Groups -
Chapter Twenty Tits Indices -
Chapter Twenty One Parallel Residues -
Chapter Twenty Two Fixed Point Buildings -
Chapter Twenty Three Subbuildings -
Chapter Twenty Four Moufang Structures -
Chapter Twenty Five Fixed Apartments -
Chapter Twenty Six The Standard Metric -
Chapter Twenty Seven Affine Fixed Point Buildings -
Chapter Twenty Eight Pseudo-Split Buildings -
Chapter Twenty Nine Linear Automorphisms -
Chapter Thirty Strictly Semi-linear Automorphisms -
Chapter Thirty One Galois Involutions -
Chapter Thirty Two Unramified Galois Involutions -
Chapter Thirty Three Residually Pseudo-Split Buildings -
Chapter Thirty Four Forms of Residually Pseudo-Split Buildings -
Chapter Thirty Five Orthogonal Buildings -
Chapter Thirty Six Indices for the Exceptional Bruhat-Tits Buildings - Bibliography
- Index
