Compact projective planes: with an introduction to octonion geometry
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
de Gruyter
1995
|
| Schriftenreihe: | De Gruyter expositions in mathematics
21 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 688 S. graph. Darst. |
| ISBN: | 3110114801 |
Internformat
MARC
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| 245 | 1 | 0 | |a Compact projective planes |b with an introduction to octonion geometry |c by Helmut Salzmann ... |
| 264 | 1 | |a Berlin [u.a.] |b de Gruyter |c 1995 | |
| 300 | |a XIII, 688 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a De Gruyter expositions in mathematics |v 21 | |
| 650 | 7 | |a Plans projectifs |2 ram | |
| 650 | 7 | |a Projectieve oppervlakken |2 gtt | |
| 650 | 4 | |a Projective planes | |
| 650 | 0 | 7 | |a Projektive Ebene |0 (DE-588)4175884-5 |2 gnd |9 rswk-swf |
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| 700 | 1 | |a Salzmann, Helmut |e Sonstige |4 oth | |
| 830 | 0 | |a De Gruyter expositions in mathematics |v 21 |w (DE-604)BV004069300 |9 21 | |
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Datensatz im Suchindex
| _version_ | 1804124837713543168 |
|---|---|
| adam_text | Contents
Preface v
Chapter 1
The classical planes 1
11 The classical division algebras 4
12 The classical affine planes 25
13 The projective planes over R, C, and H 42
14 The planes over R, C, and H as topological planes 56
15 Geometry of a projective line 65
16 The projective octonion plane 2?2© 77
17 The collineation group of 5?2O 88
18 Motion groups of 2?2O 103
Chapter 2
Background on planes, coordinates and collineations 131
21 Projective and affine planes 131
22 Coordinates, ternary fields 135
23 Collineations 137
24 Lenz Barlotti types 142
25 Translation planes and quasifields 144
Chapter 3
Geometries on surfaces 148
31 R2 planes 149
32 Two dimensional compact projective planes 163
33 Towards classification 178
34 The Moulton planes 185
35 Skew hyperbolic planes 196
36 Skew parabola planes 202
37 Planes over Cartesian fields 205
38 Flexibility, rigidity and related topics 212
xii Contents
Chapter 4
Compact projective planes 216
41 The topology of locally compact planes 217
42 Compact, connected planes 225
43 Ternary fields for compact planes 230
44 Automorphism groups 235
Chapter 5
Algebraic topology of compact, connected planes 244
51 General properties 245
52 Assuming that lines are manifolds 257
53 Conditions implying that lines are manifolds 266
54 Lines are homology manifolds 276
55 Geometric consequences 283
Chapter 6
Homogeneity 309
61 Axial collineations 311
62 Planes admitting a classical motion group 323
63 Transitive groups 339
64 Transitive axial groups 349
65 Groups of large dimension 368
66 Remarks on von Staudt s point of view 370
Chapter 7
Four dimensional planes 372
71 Automorphism groups 373
72 Characterizing SP2C 383
73 Four dimensional translation planes 393
74 Four dimensional shift planes 420
75 Analytic planes 445
Chapter 8
Eight and sixteen dimensional planes 449
81 Translation planes 452
82 Classification of translation planes 477
83 Stiffness 519
84 Characterizing ^B. 535
85 Characterizing 9P2© 547
Contents xiii
86 Hughes planes 555
87 Principles of classification 581
Chapter 9
Appendix: Tools from topology and Lie theory 590
91 Permutation groups 590
92 Topological dimension and remarks on general topology 592
93 Locally compact groups and Lie groups 597
94 Lie groups and their structure 602
95 Linear representations 616
96 Transformation groups 630
Bibliography 643
Notation 679
Index 683
|
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| id | DE-604.BV010409203 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:52:01Z |
| institution | BVB |
| isbn | 3110114801 |
| language | English |
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| physical | XIII, 688 S. graph. Darst. |
| publishDate | 1995 |
| publishDateSearch | 1995 |
| publishDateSort | 1995 |
| publisher | de Gruyter |
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| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Compact projective planes with an introduction to octonion geometry by Helmut Salzmann ... Berlin [u.a.] de Gruyter 1995 XIII, 688 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 21 Plans projectifs ram Projectieve oppervlakken gtt Projective planes Projektive Ebene (DE-588)4175884-5 gnd rswk-swf Projektive Ebene (DE-588)4175884-5 s DE-604 Salzmann, Helmut Sonstige oth De Gruyter expositions in mathematics 21 (DE-604)BV004069300 21 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006932203&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Compact projective planes with an introduction to octonion geometry De Gruyter expositions in mathematics Plans projectifs ram Projectieve oppervlakken gtt Projective planes Projektive Ebene (DE-588)4175884-5 gnd |
| subject_GND | (DE-588)4175884-5 |
| title | Compact projective planes with an introduction to octonion geometry |
| title_auth | Compact projective planes with an introduction to octonion geometry |
| title_exact_search | Compact projective planes with an introduction to octonion geometry |
| title_full | Compact projective planes with an introduction to octonion geometry by Helmut Salzmann ... |
| title_fullStr | Compact projective planes with an introduction to octonion geometry by Helmut Salzmann ... |
| title_full_unstemmed | Compact projective planes with an introduction to octonion geometry by Helmut Salzmann ... |
| title_short | Compact projective planes |
| title_sort | compact projective planes with an introduction to octonion geometry |
| title_sub | with an introduction to octonion geometry |
| topic | Plans projectifs ram Projectieve oppervlakken gtt Projective planes Projektive Ebene (DE-588)4175884-5 gnd |
| topic_facet | Plans projectifs Projectieve oppervlakken Projective planes Projektive Ebene |
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