- 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
Strictly Semi-linear Automorphisms
Strictly Semi-linear Automorphisms
- Chapter:
- (p.259) Chapter Thirty Strictly Semi-linear Automorphisms
- Source:
- Descent in Buildings (AM-190)
- Author(s):
Bernhard M¨uhlherr
Holger P. Petersson
Richard M. Weiss
- Publisher:
- Princeton University Press
This chapter considers the action of a strictly semi-linear automorphism fixing a root on the corresponding root group. It begins with the hypothesis whereby Δ is a Moufang spherical building and Π is the Coxeter diagram of Δ; here the chapter fixes an apartment Σ of Δ and a root α of Σ. The discussion then turns to a number of assumptions about an isomorphism of Moufang sets, anisotropic quadratic space, and root group sequence, followed by a lemma where E is an octonion division algebra with center F and norm N and D is a quaternion subalgebra of E. The chapter concludes with three versions of what is really one result about fixed points of non-linear automorphisms of the Moufang sets.
Keywords: strictly semi-linear automorphism, root, root group, Moufang spherical building, Coxeter diagram, apartment, Moufang set, anisotropic quadratic space, octonion division algebra, non-linear automorphism
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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
