Moufang Polygons

Moufang Polygons
Author: Jacques Tits
Publisher: Springer Science & Business Media
Total Pages: 554
Release: 2002-09-12
Genre: Mathematics
ISBN: 9783540437147

This book gives the complete classification of Moufang polygons, starting from first principles. In particular, it may serve as an introduction to the various important algebraic concepts which arise in this classification including alternative division rings, quadratic Jordan division algebras of degree three, pseudo-quadratic forms, BN-pairs and norm splittings of quadratic forms. This book also contains a new proof of the classification of irreducible spherical buildings of rank at least three based on the observation that all the irreducible rank two residues of such a building are Moufang polygons. In an appendix, the connection between spherical buildings and algebraic groups is recalled.

Generalized Polygons

Generalized Polygons
Author: Hendrik Van Maldeghem
Publisher: Springer Science & Business Media
Total Pages: 510
Release: 2012-01-05
Genre: Mathematics
ISBN: 3034802706

Generalized Polygons is the first book to cover, in a coherent manner, the theory of polygons from scratch. In particular, it fills elementary gaps in the literature and gives an up-to-date account of current research in this area, including most proofs, which are often unified and streamlined in comparison to the versions generally known. Generalized Polygons will be welcomed both by the student seeking an introduction to the subject as well as the researcher who will value the work as a reference. In particular, it will be of great value for specialists working in the field of generalized polygons (which are, incidentally, the rank 2 Tits-buildings) or in fields directly related to Tits-buildings, incidence geometry and finite geometry. The approach taken in the book is of geometric nature, but algebraic results are included and proven (in a geometric way!). A noteworthy feature is that the book unifies and generalizes notions, definitions and results that exist for quadrangles, hexagons, octagons - in the literature very often considered separately - to polygons. Many alternative viewpoints given in the book heighten the sense of beauty of the subject and help to provide further insight into the matter.​

Tits Buildings and the Model Theory of Groups

Tits Buildings and the Model Theory of Groups
Author: Katrin Tent
Publisher: Cambridge University Press
Total Pages: 314
Release: 2002-01-03
Genre: Mathematics
ISBN: 9780521010634

Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.

Translation Generalized Quadrangles

Translation Generalized Quadrangles
Author: Joseph A Thas
Publisher: World Scientific
Total Pages: 377
Release: 2006-09-28
Genre: Mathematics
ISBN: 9814477281

Translation generalized quadrangles play a key role in the theory of generalized quadrangles, comparable to the role of translation planes in the theory of projective and affine planes. The notion of translation generalized quadrangle is a local analogue of the more global “Moufang Condition”, a topic of great interest, also due to the classification of all Moufang polygons. Attention is thus paid to recent results in that direction, but also many of the most important results in the general theory of generalized quadrangles that appeared since 1984 are treated.Translation Generalized Quadrangles is essentially self-contained, as the reader is only expected to be familiar with some basic facts on finite generalized quadrangles. Proofs that are either too long or too technical are left out, or just sketched. The three standard works on generalized quadrangles are (co-)authored by the writers of this book: “Finite Generalized Quadrangles” (1984) by S E Payne and J A Thas, “Generalized Polygons” (1998) by H Van Maldeghem, and “Symmetry in Finite Generalized Quadrangles” (2004) by K Thas.

Buildings

Buildings
Author: Peter Abramenko
Publisher: Springer Science & Business Media
Total Pages: 758
Release: 2008-12-16
Genre: Mathematics
ISBN: 0387788352

This book treats Jacques Tit's beautiful theory of buildings, making that theory accessible to readers with minimal background. It covers all three approaches to buildings, so that the reader can choose to concentrate on one particular approach. Beginners can use parts of the new book as a friendly introduction to buildings, but the book also contains valuable material for the active researcher. This book is suitable as a textbook, with many exercises, and it may also be used for self-study.

The Abel Prize 2008-2012

The Abel Prize 2008-2012
Author: Helge Holden
Publisher: Springer Science & Business Media
Total Pages: 561
Release: 2014-01-21
Genre: Mathematics
ISBN: 3642394493

Covering the years 2008-2012, this book profiles the life and work of recent winners of the Abel Prize: · John G. Thompson and Jacques Tits, 2008 · Mikhail Gromov, 2009 · John T. Tate Jr., 2010 · John W. Milnor, 2011 · Endre Szemerédi, 2012. The profiles feature autobiographical information as well as a description of each mathematician's work. In addition, each profile contains a complete bibliography, a curriculum vitae, as well as photos — old and new. As an added feature, interviews with the Laureates are presented on an accompanying web site (http://extras.springer.com/). The book also presents a history of the Abel Prize written by the historian Kim Helsvig, and includes a facsimile of a letter from Niels Henrik Abel, which is transcribed, translated into English, and placed into historical perspective by Christian Skau. This book follows on The Abel Prize: 2003-2007, The First Five Years (Springer, 2010), which profiles the work of the first Abel Prize winners.

Tits Polygons

Tits Polygons
Author: Bernhard Mühlherr
Publisher: American Mathematical Society
Total Pages: 114
Release: 2022-02-02
Genre: Mathematics
ISBN: 1470451018

View the abstract.

Surveys in Combinatorics 2011

Surveys in Combinatorics 2011
Author: Robin Chapman
Publisher: Cambridge University Press
Total Pages: 447
Release: 2011-06-23
Genre: Mathematics
ISBN: 1139503685

This volume contains articles based on the invited lectures given at the 23rd British Combinatorial Conference, held in July 2011 at the University of Exeter. Each article surveys an area of current research in combinatorial mathematics and will be invaluable to anyone wishing to keep abreast of modern developments.

Finite Geometries

Finite Geometries
Author: Johnson
Publisher: CRC Press
Total Pages: 476
Release: 1983-01-18
Genre: Mathematics
ISBN: 9780824710521

The Structure of Affine Buildings. (AM-168)

The Structure of Affine Buildings. (AM-168)
Author: Richard Mark Weiss
Publisher: Princeton University Press
Total Pages: 388
Release: 2009
Genre: Architecture
ISBN: 9780691138817

Richard Weiss gives a detailed presentation of the complete proof of the classification of Bruhat-Tits buildings first completed by Jacques Tits in 1986. The book includes numerous results about automorphisms, completions and residues of these buildings.