Cantitate/Preț
Produs
Total produse
Vezi coșul
Buildings de Peter Abramenko

Buildings: Graduate Texts in Mathematics, cartea 248

Autor Peter Abramenko, Kenneth S. Brown
en Limba Engleză Paperback – 19 noi 2010

Evoluția teoriei clădirilor în ultimele decenii a transformat acest domeniu dintr-un instrument geometric auxiliar într-un pilon central al algebrei moderne, facilitând conexiuni profunde între grupurile de tip Lie și structurile combinatorii. Observăm că Buildings, publicată în prestigioasa serie Graduate Texts in Mathematics, marchează un moment de maturitate pentru acest subiect, oferind ceea ce specialiștii au numit prima resursă enciclopedică a domeniului. Lucrarea reușește să reconcilieze perspectiva tradițională — în care o clădire este văzută ca un complex simplicial — cu abordarea modernă a spațiilor W-metrice, esențială pentru aplicațiile contemporane.

Suntem de părere că rigoarea cu care este construit volumul permite o progresie naturală: se începe cu fundamentele grupurilor Coxeter și complexelor aferente (capitolele 1-3), avansând spre structuri complexe precum sistemele RGD și clădirile gemene Moufang. Această abordare completează perspectiva oferită de Lectures on Buildings, adăugând o profunzime tehnică și un aparat de exerciții mult mai vast, transformând textul dintr-o introducere prietenoasă într-un manual de referință pentru cercetare. Față de The Structure of Spherical Buildings, care se concentrează pe cazul sferic prin prisma teoriei grafurilor, volumul de față extinde analiza către clădirile euclidiene și hiperbolice, oferind un context mult mai larg.

În contextul operei autorilor, Buildings integrează și rafinează conceptele explorate de Peter Abramenko în Twin Buildings and Applications to S-Arithmetic Groups, oferind o bază teoretică solidă care lipsea din monografiile mai restrânse. Ediția de față, un reprint al versiunii din 2008, include ilustrații noi și soluții pentru exerciții, fiind adaptată nevoilor actuale ale studenților la doctorat și cercetătorilor în matematică pură.

Citește tot Restrânge

Din seria Graduate Texts in Mathematics

  • 13% Algebra
    Preț: 38943 lei
  • Measure, Integration & Real Analysis
    Preț: 38246 lei
  • 15% Unitary Representations and Unitary Duals
    Preț: 50219 lei
  • Riemannian Geometry
    Preț: 48962 lei
  • 15% Introduction to Riemannian Manifolds
    Preț: 39548 lei
  • 15% Topics in Banach Space Theory
    Preț: 53399 lei
  • 15% Differential Geometry
    Preț: 39484 lei
  • 15% Intersection Homology & Perverse Sheaves
    Preț: 42756 lei
  • 15% Basic Representation Theory of Algebras
    Preț: 39271 lei
  • 15% Spectral Theory: Basic Concepts and Applications
    Preț: 39404 lei
  • 15% Explorations in Complex Functions
    Preț: 42968 lei
  • 15% Mathematical Logic
    Preț: 42865 lei
  • 15% An Introduction to Automorphic Representations
    Preț: 39968 lei
  • 15% An Invitation to Mathematical Logic
    Preț: 46775 lei
  • 17% A Course in Real Algebraic Geometry
    Preț: 43211 lei
  • Quaternion Algebras
    Preț: 26107 lei
  • 15% Introduction to Axiomatic Set Theory
    Preț: 56238 lei
  • Harmonic Analysis on Semigroups: Theory of Positive Definite and Related Functions
    Preț: 38134 lei
  • 15% Galois Theory
    Preț: 42486 lei
  • 15% Lie Groups, Lie Algebras, and Their Representations
    Preț: 51868 lei
  • 17% Complex Analysis
    Preț: 43251 lei
  • 15% Modern Geometry- Methods and Applications
    Preț: 54038 lei
  • SL2(R)
    Preț: 48143 lei
  • The Arithmetic of Elliptic Curves
    Preț: 38521 lei
  • Applications of Lie Groups to Differential Equations
    Preț: 37519 lei
  • 15% Holomorphic Functions and Integral Representations in Several Complex Variables
    Preț: 57647 lei
  • 15% Univalent Functions and Teichmüller Spaces
    Preț: 47757 lei
  • Functions of One Complex Variable I
    Preț: 44238 lei
  • 15% Algebraic Number Theory
    Preț: 46083 lei
  • Elliptic Curves
    Preț: 48091 lei
  • 15% Elliptic Functions
    Preț: 68172 lei
  • A Course in Number Theory and Cryptography
    Preț: 43304 lei
  • 15% Differential Geometry: Manifolds, Curves, and Surfaces
    Preț: 58034 lei
  • Measure and Integral
    Preț: 37133 lei
  • 15% Algebraic Groups and Class Fields
    Preț: 56670 lei
  • 15% Analysis Now
    Preț: 51613 lei
  • 15% An Introduction to Algebraic Topology
    Preț: 49664 lei

Preț: 49601 lei

Puncte Express: 744

Carte tipărită la comandă

Livrare economică 23 mai-06 iunie

 Adaugă în coș

Wish list
Gift list
Am citit!
Adaugă în listă

Specificații

ISBN-13: 9781441927019
ISBN-10: 1441927018
Pagini: 776
Ilustrații: XXII, 754 p. 100 illus.
Dimensiuni: 155 x 235 x 42 mm
Greutate: 1.15 kg
Ediția:Softcover reprint of hardcover 1st ed. 2008
Editura: Springer
Colecția Graduate Texts in Mathematics
Seria Graduate Texts in Mathematics

Locul publicării:New York, NY, United States

Public țintă

Research

De ce să citești această carte

Recomandăm această lucrare oricărui matematician interesat de geometria grupurilor. Cititorul câștigă o viziune unitară asupra teoriei clădirilor, beneficiind de tranziția clară de la metodele clasice la cele metrice. Este o resursă esențială pentru cercetare, oferind nu doar demonstrații riguroase pentru clasificarea clădirilor sferice, ci și aplicații practice în coomologia grupurilor, fiind considerată standardul de aur în literatura de specialitate curentă.

Despre autor

Kenneth S. Brown este profesor la Cornell University din 1971, având doctoratul obținut la MIT. Este o autoritate recunoscută în topologie și algebră, lucrarea sa anterioară despre clădiri din 1989 fiind punctul de plecare pentru acest volum. Peter Abramenko, profesor la University of Virginia, este specialist în grupuri aritmetice și geometrie combinatorie. Expertiza sa în domeniul clădirilor gemene, demonstrată în publicațiile sale anterioare la Springer, completează viziunea lui Brown, cei doi formând o echipă care acoperă atât fundamentul didactic, cât și frontiera cercetării moderne în matematică.

Descriere scurtă

This text started out as a revised version of Buildings by the second-named author [53], but it has grown into a much more voluminous book. The earlier book was intended to give a short, friendly, elementary introduction to theory, accessible to readers with a minimal background.Moreover, it approached buildings from only one point of view, sometimes called the “old-fashioned” approach: A building is a simplicial complex with certain properties. The current book includes all the material of the earlier one, but we have added a lot. In particular, we have included the “modern” (or “W-metric”) approach to buildings, which looks quite different from the old-fashioned approach but is equivalent to it. This has become increasingly important in the theory and applications of buildings. We have also added a thorough treatment of the Moufang property, which occupies two chapters. And we have added many new exercises and illustrations. Some of the exercises have hints or solutions in the back of the book. A more extensive set of solutions is available in a separate solutions manual, which may be obtained from Springer’s Mathematics Editorial Department. We have tried to add the new material in such a way that readers who are content with the old-fashioned approach can still get an elementary treatment of it by reading selected chapters or sections. In particular, many readers will want to omit the optional sections (marked with a star). The introduction below provides more detailed guidance to the reader.

Cuprins

Finite Reflection Groups.- Coxeter Groups.- Coxeter Complexes.- Buildings as Chamber Complexes ..- Buildings as W-Metric Spaces.- Buildings and Groups.- Root Groups and the Moufang Property ..- Moufang Twin Buildings and RGD Systems.- The Classification of Spherical Buildings.- Euclidean and Hyperbolic Reflection Groups.- Euclidean Buildings ..- Buildings as Metric Spaces.- Applications to the Cohomology of Groups.- Other Applications.

Recenzii

From the reviews:
American Mathematical Society Mathematical Reviews MR2439729:
"The book under review ... is the first encyclopedic treatment of buildings made available in the literature, so that with writing this book the authors manage to close a serious gap in the mathematical literature: the non-existence of an easily accessible reference for buildings beyond an introduction.
In their introduction the authors state that it is their ``goal in this book to treat buildings from all three ... points of view [via the simplicial, the combinatorial, and the metric approach]. The various approaches complement one another and are useful. On the other hand, [the authors] recognize that some readers may prefer one particular viewpoint. [The authors] have therefore tried to create more than one path through the book so that, for example, the reader interested only in the combinatorial approach can learn the basics without having to spend too much time studying buildings as simplicial complexes.'' In the reviewer's opinion, the authors perfectly reach this goal and, moreover, manage to show that the theory of buildings and their applications are active, thriving, exciting and beautiful areas of mathematics. This book is very well written. The reviewer is sure that it will become a standard reference for buildings and remain one for a very long time.
... The main advantages of the combinatorial approach to buildings are that it is elementary and abstract and, hence, easily accessible. Since the simplicial and combinatorial approaches are equivalent..., one can always work with the one which is more suitable for one's own problems or more appealing to one's own taste. It is indeed one of the great achievements of this book to introduce both concepts simultaneously and to combine them in a natural way.
... Chapter 8 is extremely valuable for students and researchers interested in the theory of twin buildings, as it makes the theory... easily accessible. It is particularly important for the mathematical community that the folklore Theorem 8.27 has finally been recorded.
... Altogether, the book under review is a wonderful piece of work that will have many enthusiastic readers."
“This book is the first one which presents all of the different approaches to buildings alongside one another, and it does so in an accessible yet thorough manner which should prove extremely useful to anyone wishing to learn more about this interesting area of mathematics. The goal of presenting this introductory material in one place would be laudable enough. … this book is an extremely valuable addition to the mathematical literature. … it should also be an essential resource for experts in the area.” (Michael Bate, Zentralblatt MATH, Vol. 1214, 2011)

Notă biografică

Kenneth S. Brown has been a professor at Cornell since 1971. He received his Ph.D. in 1971 from MIT. He has published many works, including Buildings with Springer-Verlag in 1989, reprinted in 1998.
Peter Abramenko received his Ph.D. in 1987 from the University of Frankfurt, Germany. He held various academic positions afterwards, including a Heisenberg fellowship from 1998 until 2001. Since 2001, he is Associate Professor at the University of Virginia in Charlottesville. He has previously published Twin Buildings and Applications to S-Arithmetic Groups for the Lecture Notes in Mathematics series for Springer (1996).

Textul de pe ultima copertă

This book treats Jacques Tits's beautiful theory of buildings, making that theory accessible to readers with minimal background. It includes all the material of the earlier book Buildings by the second-named author, published by Springer-Verlag in 1989, which gave an introduction to buildings from the classical (simplicial) point of view. This new book also includes two other approaches to buildings, which nicely complement the simplicial approach: On the one hand, buildings may be viewed as abstract sets of chambers with a Weyl-group-valued distance function; this point of view has become increasingly important in the theory and applications of buildings. On the other hand, buildings may be viewed as metric spaces. Beginners can still use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher.
There are several paths through the book, so that readers may choose to concentrate onone particular approach. The pace is gentle in the elementary parts of the book, and the style is friendly throughout. All concepts are well motivated. There are thorough treatments of advanced topics such as the Moufang property, with arguments that are much more detailed than those that have previously appeared in the literature.
This book is suitable as a textbook, with many exercises, and it may also be used for self-study.

Caracteristici

Contains all of the material from the previous book, Buildings by K. S. Brown (a short, friendly, elementary introduction to the theory of buildings), and substantially revised, updated, new material Includes advanced content that is appropriate for more advanced students or for self-study, including two new chapters on the Moufang propert Introduces many new exercises and illustrations, as well as hints and solutions--including a separate, extensive solutions manual Thoroughly focuses on all three approachs to buildings, “old-fashioned," combinatorial (chamber systems), and metric so that the reader can learn all three or focus on only one Includes appendices on cell complexes, root systems and algebraic groups Request lecturer material: sn.pub/lecturer-material