Jacques Tits,
Richard M. Weiss
Springer Berlin Heidelberg
0e druk, 2010
9783642078330
Moufang Polygons
Specificaties
Paperback, 535 blz.
|
Engels
Springer Berlin Heidelberg |
2010
ISBN13: 9783642078330
Rubricering
Onderdeel van serie
Springer Monographs in Mathematics
Levertijd ongeveer 9 werkdagen
Gratis verzonden
Samenvatting
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.
Specificaties
ISBN13:9783642078330
Taal:Engels
Bindwijze:paperback
Aantal pagina's:535
Uitgever:Springer Berlin Heidelberg
Druk:0
Inhoudsopgave
I Preliminary Results.- 1 Introduction.- 2 Some Definitions.- 3 Generalized Polygons.- 4 Moufang Polygons.- 5 Commutator Relations.- 6 Opposite Root Groups.- 7 A Uniqueness Lemma.- 8 A Construction.- II Nine Families of Moufang Polygons.- 9 Alternative Division Rings, I.- 10 Indifferent and Octagonal Sets.- 11 Involutory Sets and Pseudo-Quadratic Forms.- 12 Quadratic Forms of Type E6, E7 and E8, I.- 13 Quadratic Forms of Type E6, E7 and E8, II.- 14 Quadratic Forms of Type F4.- 15 Hexagonal Systems, I.- 16 An Inventory of Moufang Polygons.- 17 Main Results.- III The Classification of Moufang Polygons.- 18 A Bound on n.- 19 Triangles.- 20 Alternative Division Rings, II.- 21 Quadrangles.- 22 Quadrangles of Involution Type.- 23 Quadrangles of Quadratic Form Type.- 24 Quadrangles of Indifferent Type.- 25 Quadrangles of Pseudo-Quadratic Form Type, I.- 26 Quadrangles of Pseudo-Quadratic Form Type, II.- 27 Quadrangles of Type E6, E7 and E8.- 28 Quadrangles of Type F4.- 29 Hexagons.- 30 Hexagonal Systems, II.- 31 Octagons.- 32 Existence.- IV More Results on Moufang Polygons.- 33 BN-Pairs.- 34 Finite Moufang Polygons.- 35 Isotopes.- 36 Isomorphic Hexagonal Systems.- 37 Automorphisms.- 38 Isomorphic Quadrangles.- V Moufang Polygons and Spherical Buildings.- 39 Chamber Systems.- 40 Spherical Buildings.- 41 Classical, Algebraic and Mixed Buildings.- 42 Appendix.- Index of Notation.