Lectures on Buildings

In mathematics, "buildings" are geometric structures that represent groups of Lie type over an arbitrary field. This concept is critical to physicists and mathematicians working in discrete mathematics, simple groups, and algebraic group theory, to name just a few areas. Almost twenty years after its original publication, Mark Ronan'sLectures on Buildingsremains one of the best introductory texts on the subject. A thorough, concise introduction to mathematical buildings, it contains problem sets and an excellent bibliography that will prove invaluable to students new to the field.Lectures on Buildingswill find a grateful audience among those doing research or teaching courses on Lie-type groups, on finite groups, or on discrete groups. "Ronan's account of the classification of affine buildings [is] both interesting and stimulating, and his book is highly recommended to those who already have some knowledge and enthusiasm for the theory of buildings."Bulletin of the London Mathematical Society

Mark Ronan is Emeritus Professor at the University of Illinois at Chicago and Honorary Professor of Mathematics at University College, London. He is the author of Symmetry and the Monster.

Introduction to the 2009 Edition	p. x
Introduction	p. xi
Leitfaden	p. xiii
Chamber Systems And Examples
Buildings and the Origin of Chamber Systems	p. 1
Chamber Systems	p. 2
Two Examples of Buildings	p. 3
Exercises	p. 7
Coxeter Complexes
Coxeter Groups and Complexes	p. 9
Words and Galleries	p. 12
Reduced Words and Homotopy	p. 17
Finite Coxeter Complexes	p. 19
Self-Homotopy	p. 22
Exercises	p. 24
Buildings
A Definition of Buildings	p. 27
Generalized m-gons - the rank 2 case	p. 28
Residues and Apartments	p. 30
Exercises	p. 35
Local Properties And Coverings
Chamber Systems of Type M	p. 39
Coverings and the Fundamental Group	p. 41
The Universal Cover	p. 44
Examples	p. 47
Exercises	p. 51
BN - Paris
Tits Systems and Buildings	p. 55
Parabolic Subgroups	p. 59
Exercises	p. 61
Buildings Of Spherical Type And Root Groups
Some Basic Lemmas	p. 63
Root Groups and the Moufang Property	p. 66
Commutator Relationships	p. 68
Moufang Buildings - the general case	p. 73
Exercises	p. 80
A Construction Of Buildings
Blueprints	p. 83
Natural Labellings of Moufang Buildings	p. 86
Foundations	p. 89
Exercises	p. 91
The Classification Of Spherical Buildings
A3 Blueprints and Foundations	p. 92
Diagrams with Single Bonds	p. 94
C3 Foundations	p. 97
Cn Buildings for n ? 4	p. 98
Tits Diagrams and F4 Buildings	p. 100
Finite Buildings	p. 106
Exercises	p. 108
Affine Buildings I
Affine Coxeter Complexes and Sectors	p. 110
The Affine Building Ãn-1(K,v)	p. 114
The Spherical Building at Infinity	p. 120
The Proof of(9.5)	p. 124
Exercises	p. 127
Affine Buildings II
Apartment Systems, Trees and Projective Valuations	p. 129
Trees associated to Walls and Panels at Infinity	p. 133
Root Groups with a Valuation	p. 138
Construction of an Affine BN-Pair	p. 144
The Classification	p. 152
An Application	p. 157
Exercises	p. 160
Twin Buildings
Twin Buildings and Kac-Moody Groups	p. 162
Twin Trees	p. 165
Twin Apartments	p. 167
An Example: Affine Twin Buildings	p. 170
Residues, Rigidity, and Proj.	p. 172
2-Spherical Twin Buildings	p. 174
The Moufang Property and Root Group Data	p. 178
Twin Trees Again	p. 182
Moufang Polygons
The m-function	p. 184
The Natural Labelling for a Moufang Plane	p. 187
The Non-existence Theorem	p. 190
Diagrams For Moufang Polygons	p. 197
Non-Discrete Buildings	p. 202
Topology And The Steinberg Representation	p. 206
Finite Coxeter Groups	p. 212
Finite Buildings And Groups Of Lie Type	p. 213
Bibliography	p. 216
Index Of Notation	p. 223
Index	p. 22
Table of Contents provided by Ingram. All Rights Reserved.

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Lectures on Buildings

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