.V-, Moufang Polygons - GBV
Transcript of .V-, Moufang Polygons - GBV
Table of Contents
Part I Preliminary Results
1 Introduction 3
2 Some Definitions 7
3 Generalized Polygons 15
4 Moufang Polygons 19
5 Commutator Relations 23
6 Opposite Root Groups 27
7 A Uniqueness Lemma 31
8 A Construction 33
Part II Nine Families of Moufang Polygons
9 Alternative Division Rings, I 45
10 Indifferent and Octagonal Sets 57
11 Involutory Sets and Pseudo-Quadratic Forms 61
12 Quadratic Forms of Type Ee, E7 and E$, I 71
13 Quadratic Forms of Type Ee, E7 and E&, II 91
14 Quadratic Forms of Type F4 125
15 Hexagonal Systems, I 133
16 An Inventory of Moufang Polygons 163
17 Main Results 175
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Part III The Classification of Moufang Polygons
18 A Bound o n n 179
19 Triangles 185
20 Alternative Division Rings, II 191
21 Quadrangles 203
22 Quadrangles of Involution Type 215
23 Quadrangles of Quadratic Form Type 229
24 Quadrangles of Indifferent Type 239
25 Quadrangles of Pseudo-Quadratic Form Type, I 243
26 Quadrangles of Pseudo-Quadratic Form Type, II 251
27 Quadrangles of Type E6, E7 and Es 275
28 Quadrangles of Type FA 285
29 Hexagons 301
30 Hexagonal Systems, II 319
31 Octagons 339
32 Existence 353
Part IV More Results on Moufang Polygons
33 BN-Pairs 367
34 Finite Moufang Polygons 375
35 Isotopes 381
36 Isomorphic Hexagonal Systems 391
37 Automorphisms 397
38 Isomorphic Quadrangles 419
Table of Contents ix
Part V Moufang Polygons and Spherical Buildings
39 Chamber Systems 427
40 Spherical Buildings 447
41 Classical, Algebraic and Mixed Buildings 477
42 Appendix 489
Bibliography 521
Index of Notation 527
Index 529
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