Moufang Polygons

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.

From the reviews: "In this excellently written book, the authors give a full classification for Moufang polygons. … The book is self contained … . the content of the book is accessible for motivated graduate students and researchers from every branch of mathematics. We recommend this book for everybody who is interested in the developments of the modern algebra, geometry or combinatorics." (Gábor P. Nagy, Acta Scientiarum Mathematicarum, Vol. 71, 2005) "The publication of this long-awaited book is a major event for geometry in general, and for the theory of buildings in particular. … The classifications established in this book are splendid achievements of fundamental significance. The whole book is extremely well written, in a clear and concise style … . It is the definitive treatment and a standard reference." (Theo Grundhöfer, Mathematical Reviews, Issue 2003 m) "This book contains the complete classification of all Moufang generalized polygons, including the full proof. … So, in conclusion, the book is a Bible for everyone interested in classification results related to spherical buildings. It is written in a very clear and concise way. It should be in the library of every mathematician as one of the major results in the theory of (Tits) buildings, (combinatorial) incidence geometry and (algebraic) group theory." (Hendrik Van Maldeghem, Bulletin of the Belgian Mathematical Society, Vol. 11 (3), 2005)