Lectures on Buildings: Updated and Revised

✍ Scribed by Mark Ronan

• Publisher: University of Chicago Press
• Year: 2009
• Tongue: English
• Leaves: 240
• Edition: Updated, Revised
• Category: Library

✦ Synopsis

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’s Lectures on Buildings remains 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 Buildings will 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

✦ Table of Contents

Contents
Introduction to the 2009 Edition
Introduction
Leitfaden
Chapter 1 Chamber syetems and examples
Chapter 2 Coxeter complexes
Chapter 3 Buildings
Chapter 4 Local properties and coverings
Chapter 5 BN-pairs
Chapter 6 Buildings of spherical types and root groups
Chapter 7 A construction of buildings
Chapter 8 The classification of spherical buildings
Chapter 9 Affine buildings I
Chapter 10 Affine buildings II
Chapter 11 Twin buildings
Appendix 1 Moufang polygons
Appendix 2 Diagrams for Moufang polygons
Appendix 3 Non-discrete buildings
Appendix 4 Topology and Steinberg representation
Appendix 5 Finite Coxeter groups (i.e. of spherical type)
Bibliography
Index of notation
Index