Diagram geometry: related to classical groups and buildings
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2013
|
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
3. Folge ; 57 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Item Description: | Literaturverz. S. 571 - 583 |
| Physical Description: | XIII, 592 S. graph. Darst. 235 mm x 155 mm |
| ISBN: | 3642344526 9783642344527 |
Staff View
MARC
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| 245 | 1 | 0 | |a Diagram geometry |b related to classical groups and buildings |c Francis Buekenhout ; Arjeh M. Cohen |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2013 | |
| 300 | |a XIII, 592 S. |b graph. Darst. |c 235 mm x 155 mm | ||
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| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge |v 57 | |
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| 650 | 0 | 7 | |a Diagramm-Geometrie |0 (DE-588)4792060-9 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Diagramm-Geometrie |0 (DE-588)4792060-9 |D s |
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| 700 | 1 | |a Cohen, Arjeh M. |d 1949- |e Verfasser |0 (DE-588)121202119 |4 aut | |
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Record in the Search Index
| _version_ | 1804150175059410944 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
1 GEOMETRIES 1
1.1 THE CONCEPT OF A GEOMETRY 1
1.2 INCIDENCE SYSTEMS AND GEOMETRIES 4
1.3 HOMOMORPHISMS 8
1.4 SUBGEOMETRIES AND TRUNCATIONS 12
1.5 RESIDUES 18
1.6 CONNECTEDNESS 2 0
1.7 PERMUTATION GROUPS 22
1.8 GROUPS AND GEOMETRIES 29
1.9 EXERCISES 38
1.10 NOTES 45
2 DIAGRAMS 49
2.1 THE DIGON DIAGRAM O F A GEOMETRY 49
2.2 SOME PARAMETERS FOR RANK TWO GEOMETRIES 54
2.3 DIAGRAMS FOR HIGHER RANK GEOMETRIES 63
2.4 COXETER DIAGRAMS 69
2.5 SHADOWS 75
2.6 GROUP DIAGRAMS 81
2.7 A GEOMETRY OF TYPE A - I 83
2.8 EXERCISES 9 0
2.9 NOTES 99
3 CHAMBER SYSTEMS 103
3.1 FROM A GEOMETRY TO A CHAMBER SYSTEM 103
3.2 RESIDUES 109
3.3 FROM CHAMBER SYSTEMS TO GEOMETRIES I L L
3.4 CONNECTEDNESS 114
3.5 THE DIAGRAM OF A CHAMBER SYSTEM 119
3.6 GROUPS AND CHAMBER SYSTEMS 121
3.7 EXERCISES 127
3.8 NOTES 131
X I
HTTP://D-NB.INFO/1026468183
IMAGE 2
133
133 144 151
157 164 175 180
185 188 197
201 201 207 214 2 1 8
223 231 239 247
253 253 259 267
272 278 282 283
296 301
305 306 309 318 323
329 333 336 340 346
356 359 366
THIN GEOMETRIES 4.1 BEING THIN 4.2 THIN GEOMETRIES OF COXETER TYPE 4.3
GROUPS GENERATED BY AFFINE REFLECTIONS . . . 4.4 LINEAR REFLECTION
REPRESENTATIONS 4.5 ROOT SYSTEMS
4.6 FINITENESS CRITERIA 4.7 FINITE COXETER GROUPS 4.8 REGULAR POLYTOPES
REVISITED 4.9 EXERCISES 4.10 NOTES
LINEAR GEOMETRIES 5.1 THE AFFINE SPACE O F A VECTOR SPACE 5.2 THE
PROJECTIVE SPACE OF A VECTOR SPACE . . . . 5.3 MATROIDS 5.4 MATROIDS
FROM GEOMETRIES 5.5 STEINER SYSTEMS 5.6 GEOMETRIES RELATED TO THE GOLAY
CODE . . . .
5.7 EXERCISES 5.8 NOTES
PROJECTIVE AND AFFINE SPACES 6.1 PERSPECTIVITIES 6.2 PROJECTIVE LINES
6.3 CLASSIFICATION O F PROJECTIVE SPACES 6.4 CLASSIFICATION O F AFFINE
SPACES 6.5 APARTMENTS
6.6 GRASSMANNIAN GEOMETRY 6.7 ROOT FILTRATION SPACES 6.8 EXERCISES 6.9
NOTES
POLAR SPACES 7.1 DUALITY FOR GEOMETRIES OVER A LINEAR DIAGRAM 7.2
DUALITY AND SESQUILINEAR FORMS 7.3 ABSOLUTES AND REFLEXIVE SESQUILINEAR
FORMS . 7.4 POLAR SPACES 7.5 THE DIAGRAM O F A POLAR SPACE
7.6 FROM DIAGRAM TO SPACE 7.7 SINGULAR SUBSPACES 7.8 OTHER SHADOW SPACES
OF POLAR GEOMETRIES . . 7.9 ROOT FILTRATION SPACES 7.10 POLAR SPACES
WITH THIN LINES
7.11 EXERCISES 7.12 NOTES
IMAGE 3
CONTENTS XIII
8 PROJECTIVE EMBEDDINGS O F POLAR SPACES 369
8.1 GEOMETRIC HYPERPLANES AND AMPLE CONNECTEDNESS 370
8.2 THE VELDKAMP SPACE 374
8.3 PROJECTIVE EMBEDDING FOR RANK AT LEAST FOUR 378
8.4 PROJECTIVE EMBEDDING FOR RANK THREE 386
8.5 AUTOMORPHISMS OF POLAR SPACES 399
8.6 EXERCISES 405
8.7 NOTES 408
9 EMBEDDING POLAR SPACES IN ABSOLUTES 411
9.1 EMBEDDED SPACES 412
9.2 COLLARS AND TANGENT HYPERPLANES 416
9.3 A QUASI-POLARITY 423
9.4 TECHNICAL RESULTS ON DIVISION RINGS 428
9.5 EMBEDDING IN 3-DIMENSIONAL SPACE 431
9.6 EXERCISES 442
9.7 NOTES 444
10 CLASSICAL POLAR SPACES 447
10.1 TRACE VALUED FORMS 448
10.2 PSEUDO-QUADRICS 454
10.3 PERSPECTIVE SETS 462
10.4 APARTMENTS 468
10.5 AUTOMORPHISMS 475
10.6 FINITE CLASSICAL POLAR SPACES 479
10.7 EXERCISES 489
10.8 NOTES 496
11 BUILDINGS 499
11.1 BUILDING AXIOMS 500
11.2 PROPERTIES OF BUILDINGS 509
11.3 TITS SYSTEMS 514
11.4 SHADOW SPACES 522
11.5 PARAPOLAR SPACES 533
11.6 ROOT SHADOW SPACES 552
11.7 RECOGNIZING SHADOW SPACES OF BUILDINGS 554
11.8 EXERCISES 559
11.9 NOTES 565
REFERENCES 571
INDEX 585
|
| any_adam_object | 1 |
| author | Buekenhout, Francis 1937- Cohen, Arjeh M. 1949- |
| author_GND | (DE-588)1032725141 (DE-588)121202119 |
| author_facet | Buekenhout, Francis 1937- Cohen, Arjeh M. 1949- |
| author_role | aut aut |
| author_sort | Buekenhout, Francis 1937- |
| author_variant | f b fb a m c am amc |
| building | Verbundindex |
| bvnumber | BV040892268 |
| classification_rvk | SK 380 |
| ctrlnum | (OCoLC)830941447 (DE-599)DNB1026468183 |
| dewey-full | 516.11 516.5 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516.11 516.5 |
| dewey-search | 516.11 516.5 |
| dewey-sort | 3516.11 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV040892268 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T00:34:44Z |
| institution | BVB |
| isbn | 3642344526 9783642344527 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-025871894 |
| oclc_num | 830941447 |
| open_access_boolean | |
| owner | DE-83 DE-20 DE-19 DE-BY-UBM DE-11 |
| owner_facet | DE-83 DE-20 DE-19 DE-BY-UBM DE-11 |
| physical | XIII, 592 S. graph. Darst. 235 mm x 155 mm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge |
| spelling | Buekenhout, Francis 1937- Verfasser (DE-588)1032725141 aut Diagram geometry related to classical groups and buildings Francis Buekenhout ; Arjeh M. Cohen Berlin [u.a.] Springer 2013 XIII, 592 S. graph. Darst. 235 mm x 155 mm txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge 57 Literaturverz. S. 571 - 583 Diagramm-Geometrie (DE-588)4792060-9 gnd rswk-swf Diagramm-Geometrie (DE-588)4792060-9 s DE-604 Cohen, Arjeh M. 1949- Verfasser (DE-588)121202119 aut Erscheint auch als Online-Ausgabe 978-3-642-34453-4 Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge ; 57 (DE-604)BV000899194 57 DE-601 pdf/application http://www.gbv.de/dms/bs/toc/727429086.pdf Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025871894&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Buekenhout, Francis 1937- Cohen, Arjeh M. 1949- Diagram geometry related to classical groups and buildings Ergebnisse der Mathematik und ihrer Grenzgebiete Diagramm-Geometrie (DE-588)4792060-9 gnd |
| subject_GND | (DE-588)4792060-9 |
| title | Diagram geometry related to classical groups and buildings |
| title_auth | Diagram geometry related to classical groups and buildings |
| title_exact_search | Diagram geometry related to classical groups and buildings |
| title_full | Diagram geometry related to classical groups and buildings Francis Buekenhout ; Arjeh M. Cohen |
| title_fullStr | Diagram geometry related to classical groups and buildings Francis Buekenhout ; Arjeh M. Cohen |
| title_full_unstemmed | Diagram geometry related to classical groups and buildings Francis Buekenhout ; Arjeh M. Cohen |
| title_short | Diagram geometry |
| title_sort | diagram geometry related to classical groups and buildings |
| title_sub | related to classical groups and buildings |
| topic | Diagramm-Geometrie (DE-588)4792060-9 gnd |
| topic_facet | Diagramm-Geometrie |
| url | http://www.gbv.de/dms/bs/toc/727429086.pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025871894&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000899194 |
| work_keys_str_mv | AT buekenhoutfrancis diagramgeometryrelatedtoclassicalgroupsandbuildings AT cohenarjehm diagramgeometryrelatedtoclassicalgroupsandbuildings |
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