Lectures on Buildings: Updated and Revised

Paperback (Print)
Buy New
Buy New from BN.com
$42.75
Used and New from Other Sellers
Used and New from Other Sellers
from $28.60
Usually ships in 1-2 business days
(Save 36%)
Other sellers (Paperback)
  • All (11) from $28.60   
  • New (8) from $42.89   
  • Used (3) from $28.60   

Overview

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

Read More Show Less

Product Details

  • ISBN-13: 9780226724997
  • Publisher: University of Chicago Press
  • Publication date: 10/15/2009
  • Edition description: Updated
  • Pages: 248
  • Product dimensions: 6.00 (w) x 9.10 (h) x 0.60 (d)

Meet the Author

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.

Read More Show Less

Table of Contents

introduction to the 2009 edition

introduction

leitfaden

chapter 1 - chamber systems and examples

1. chamber systems

2. two examples of buildings

exercises

chapter 2 - coxeter complexes

1. coxeter groups and complexes

2. words and galleries

3. reduced words and homotopy

4. finite coxeter complexes

5. self-homotopy

exercises

chapter 3 - buildings

1. a definition of buildings

2. generalised m-gons - the rank 2 case

3. residues and apartments

exercises

chapter 4 - local properties and coverings

1. chamber systems of type m

2. coverings and the fundamental group

3. the universal cover

4. examples

exercises

chapter 5 - bn - pairs

1. tits systems and buildings

2. parabolic subgroups

exercises

chapter 6 - buildings of spherical type and root groups

1. some basic lemmas

2. root groups and the moufang property

3. commutator relations

4. moufang buildings - the general case

exercises 80

chapter 7 - a construction of buildings

1. blueprints

2. natural labellings of moufang buildings

3. foundations

exercises

chapter 8 - the classification of spherical buildings

1.a3 blueprints and foundations

2. diagrams with single bonds

3. c3 foundations

4. cn buildings for n > 4

5. tits diagrams and f4 buildings

6. finite buildings

exercises

chapter 9 - affine buildings I

1. affine coxeter complexes and sectors

2. the affine building an-1 (k,v)

3. the spherical building at infinity

4. the proof of (9.5)

exercises

chapter 10 - affine buildings II

1. apartment systems, trees and projective valuations

2. trees associated to walls and panels at infinity

3. root groups with a valuation

4. construction of an affine bn-pair

5. the classification

6. an application

exercises

chapter 11 - twin buildings

1. twin buildings and kac-moody groups

2. twin trees

3. twin apartments

4. an example: affine twin buildings

5. residues, rigidity, and proj.

6. 2-spherical twin buildings

7. the moufang property and root group data

8. twin trees again

appendix 1 - moufang polygons

1. the m-function

2. the natural labelling for a moufang plane

3. the non-existence theorem

appendix 2 - diagrams for moufang polygons

appendix 3 - non-discrete buildings

appendix 4 - topology and the steinberg representation

appendix 5 - finite coxeter groups

appendix 6 finite buildings and groups of lie type

bibliography

index of notation

index

Read More Show Less

Customer Reviews

Be the first to write a review
( 0 )
Rating Distribution

5 Star

(0)

4 Star

(0)

3 Star

(0)

2 Star

(0)

1 Star

(0)

Your Rating:

Your Name: Create a Pen Name or

Barnes & Noble.com Review Rules

Our reader reviews allow you to share your comments on titles you liked, or didn't, with others. By submitting an online review, you are representing to Barnes & Noble.com that all information contained in your review is original and accurate in all respects, and that the submission of such content by you and the posting of such content by Barnes & Noble.com does not and will not violate the rights of any third party. Please follow the rules below to help ensure that your review can be posted.

Reviews by Our Customers Under the Age of 13

We highly value and respect everyone's opinion concerning the titles we offer. However, we cannot allow persons under the age of 13 to have accounts at BN.com or to post customer reviews. Please see our Terms of Use for more details.

What to exclude from your review:

Please do not write about reviews, commentary, or information posted on the product page. If you see any errors in the information on the product page, please send us an email.

Reviews should not contain any of the following:

  • - HTML tags, profanity, obscenities, vulgarities, or comments that defame anyone
  • - Time-sensitive information such as tour dates, signings, lectures, etc.
  • - Single-word reviews. Other people will read your review to discover why you liked or didn't like the title. Be descriptive.
  • - Comments focusing on the author or that may ruin the ending for others
  • - Phone numbers, addresses, URLs
  • - Pricing and availability information or alternative ordering information
  • - Advertisements or commercial solicitation

Reminder:

  • - By submitting a review, you grant to Barnes & Noble.com and its sublicensees the royalty-free, perpetual, irrevocable right and license to use the review in accordance with the Barnes & Noble.com Terms of Use.
  • - Barnes & Noble.com reserves the right not to post any review -- particularly those that do not follow the terms and conditions of these Rules. Barnes & Noble.com also reserves the right to remove any review at any time without notice.
  • - See Terms of Use for other conditions and disclaimers.
Search for Products You'd Like to Recommend

Recommend other products that relate to your review. Just search for them below and share!

Create a Pen Name

Your Pen Name is your unique identity on BN.com. It will appear on the reviews you write and other website activities. Your Pen Name cannot be edited, changed or deleted once submitted.

 
Your Pen Name can be any combination of alphanumeric characters (plus - and _), and must be at least two characters long.

Continue Anonymously

    If you find inappropriate content, please report it to Barnes & Noble
    Why is this product inappropriate?
    Comments (optional)