The geometry of the classical groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Heldermann
1992
|
| Schriftenreihe: | Sigma series in pure mathematics
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 229 S. |
| ISBN: | 3885380099 |
Internformat
MARC
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| 100 | 1 | |a Taylor, Donald E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a The geometry of the classical groups |c Donald E. Taylor |
| 264 | 1 | |a Berlin |b Heldermann |c 1992 | |
| 300 | |a 229 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Sigma series in pure mathematics |v 9 | |
| 650 | 7 | |a Correspondance Klein |2 Jussieu | |
| 650 | 7 | |a Couple BN |2 Jussieu | |
| 650 | 7 | |a Groupe A7 |2 Jussieu | |
| 650 | 7 | |a Groupe Coxeter |2 Jussieu | |
| 650 | 7 | |a Groupe Suzuki |2 Jussieu | |
| 650 | 7 | |a Groupe Weyl |2 Jussieu | |
| 650 | 7 | |a Groupe orthogonal |2 Jussieu | |
| 650 | 7 | |a Groupe symplectique |2 Jussieu | |
| 650 | 7 | |a Groupe unitaire |2 Jussieu | |
| 650 | 7 | |a Groupes, théorie des |2 ram | |
| 650 | 7 | |a Géométrie affine |2 Jussieu | |
| 650 | 7 | |a Géométrie algébrique |2 ram | |
| 650 | 7 | |a Géométrie groupe classique |2 Jussieu | |
| 650 | 7 | |a Géométrie projective |2 Jussieu | |
| 650 | 7 | |a Immeuble Tits |2 Jussieu | |
| 650 | 7 | |a Théorème Witt |2 Jussieu | |
| 650 | 4 | |a Geometry, Algebraic | |
| 650 | 4 | |a Group theory | |
| 650 | 0 | 7 | |a Geometrie |0 (DE-588)4020236-7 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Klassische Gruppe |0 (DE-588)4164040-8 |2 gnd |9 rswk-swf |
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| 689 | 1 | 1 | |a Geometrie |0 (DE-588)4020236-7 |D s |
| 689 | 1 | |5 DE-604 | |
| 830 | 0 | |a Sigma series in pure mathematics |v 9 |w (DE-604)BV000012120 |9 9 | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-003489304 | ||
Datensatz im Suchindex
| _version_ | 1804119782929203200 |
|---|---|
| adam_text | Contents
Preface v
1 Groups Acting on Sets 1
Exercises 4
2 Affine Geometry 6
Semilinear Transformations 7
The Affine Group 9
Exercises 10
3 Projective Geometry 13
Axioms for Projective Geometry 15
Exercises 16
4 The General and Special Linear Groups 18
The Dual Space 18
The Groups SL(V) and PSL(V) 19
Order Formulae 19
The Action of PSL(V) on V{V) 20
Transvections 20
The Simplicity of PSL(V) 22
The Groups PSL(2, q) 23
Exercises 25
5 BN pairs and Buildings 27
The SiV pair Axioms 27
The Tits Building 28
The SAT pair of SL(V) 28
Chambers 30
Flags and Apartments 30
Panels 32
Split BAT pairs 33
Commutator Relations 34
The Weyl Group 35
Exercises 36
The Geometry of The Classical Groups
6 The 7 Point Plane and the Group A7 40
The 7 Point Plane 40
The Simple Group of Order 168 41
A Geometry of 7 Point Planes 43
A Geometry for As 45
Exercises 46
7 Polar Geometry 50
The Dual Space 50
Correlations 51
Sesquilinear Forms 52
Polarities 53
Quadratic Forms 54
Witt s Theorem 55
Bases of Orthogonal Hyperbolic Pairs 59
The Group ri*(V) 60
Flags and Frames 61
The Building of a Polarity 63
Exercises 65
8 Symplectic Groups 68
Matrices 68
Symplectic Bases 69
Order Formulae 70
The Action of PSp(V) on V{V) 70
Symplectic Transvections 71
The Simplicity of PSp(V) 72
Symmetric Groups 74
Symplectic 5iV pairs 75
Symplectic Buildings 77
Exercises 78
9 BN pairs, Diagrams and Geometries 83
The £iV pair of a Polar Building 83
The Weyl Group 87
Coxeter Groups 90
The Exchange Condition 91
Reflections and the Strong Exchange Condition 94
Parabolic Subgroups of Coxeter Groups 96
Complexes 97
Coxeter Complexes 98
Buildings 99
Contents
Chamber Systems 101
Diagram Geometries 103
Abstract Polar Spaces 107
Exercises 108
10 Unitary Groups 114
Matrices 114
The Field F 115
Hyperbolic Pairs 116
Order Formulae 117
Unitary Transvections 118
Hyperbolic Lines 119
The Action of PSU(V) on Isotropic Points 120
Three Dimensional Unitary Groups 121
The Group PSU(3,2) 123
The Group 5(7(4,2) 125
The Simplicity of PSU(V) 127
An Example 130
Unitary SAT pairs 130
Exercises 131
11 Orthogonal Groups 136
Matrices 137
Finite Fields 138
Order Formulae, I 140
Three Dimensional Orthogonal Groups 142
Degenerate Polar Forms and the Group O(2m + 1,2fc) 143
Reflections 144
Root Groups 146
Siegel Transformations 148
The Action of PQ,(V) on Singular Points 150
Wall s Parametrization of 0{V) 153
Factorization Theorems 155
The Generation of O(V) by Reflections 156
Dickson s Invariant 160
The Simplicity of PCl(V) 160
The Spinor Norm 163
Order Formulae, II 165
The Groups Pfi(2m + 1, q), q odd 166
Orthogonal BAT pairs 168
Maximal Totally Singular Subspaces 170
The Oriflamme Geometry 172
Exercises 174
The Geometry of The Classical Groups
12 The Klein Correspondence 179
The Exterior Algebra of a Vector Space 180
The Dual Space 183
Decomposable vectors 183
Creation and Annihilation Operators 184
The Klein Quadric 187
The Groups SL(V) and fi(A2(V)) 190
Correlations 191
Alternating Forms and Reflections 195
Hermitian Forms of Witt Index 2 196
Four Dimensional Orthogonal Groups 199
Generalized Quadrangles and Duality 201
The Suzuki Groups 202
Exercises 207
Bibliography 213
Index of Symbols 221
Index of Names 223
Index 225
|
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| dewey-ones | 512 - Algebra |
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| dewey-search | 512/.2 |
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| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Book |
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| id | DE-604.BV005568430 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:31:40Z |
| institution | BVB |
| isbn | 3885380099 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-003489304 |
| oclc_num | 26769296 |
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| owner | DE-12 DE-384 DE-739 DE-703 DE-824 DE-29T DE-91G DE-BY-TUM DE-20 DE-634 DE-83 DE-11 DE-188 |
| owner_facet | DE-12 DE-384 DE-739 DE-703 DE-824 DE-29T DE-91G DE-BY-TUM DE-20 DE-634 DE-83 DE-11 DE-188 |
| physical | 229 S. |
| publishDate | 1992 |
| publishDateSearch | 1992 |
| publishDateSort | 1992 |
| publisher | Heldermann |
| record_format | marc |
| series | Sigma series in pure mathematics |
| series2 | Sigma series in pure mathematics |
| spelling | Taylor, Donald E. Verfasser aut The geometry of the classical groups Donald E. Taylor Berlin Heldermann 1992 229 S. txt rdacontent n rdamedia nc rdacarrier Sigma series in pure mathematics 9 Correspondance Klein Jussieu Couple BN Jussieu Groupe A7 Jussieu Groupe Coxeter Jussieu Groupe Suzuki Jussieu Groupe Weyl Jussieu Groupe orthogonal Jussieu Groupe symplectique Jussieu Groupe unitaire Jussieu Groupes, théorie des ram Géométrie affine Jussieu Géométrie algébrique ram Géométrie groupe classique Jussieu Géométrie projective Jussieu Immeuble Tits Jussieu Théorème Witt Jussieu Geometry, Algebraic Group theory Geometrie (DE-588)4020236-7 gnd rswk-swf Klassische Gruppe (DE-588)4164040-8 gnd rswk-swf Klassische Gruppe (DE-588)4164040-8 s DE-604 Geometrie (DE-588)4020236-7 s Sigma series in pure mathematics 9 (DE-604)BV000012120 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003489304&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Taylor, Donald E. The geometry of the classical groups Sigma series in pure mathematics Correspondance Klein Jussieu Couple BN Jussieu Groupe A7 Jussieu Groupe Coxeter Jussieu Groupe Suzuki Jussieu Groupe Weyl Jussieu Groupe orthogonal Jussieu Groupe symplectique Jussieu Groupe unitaire Jussieu Groupes, théorie des ram Géométrie affine Jussieu Géométrie algébrique ram Géométrie groupe classique Jussieu Géométrie projective Jussieu Immeuble Tits Jussieu Théorème Witt Jussieu Geometry, Algebraic Group theory Geometrie (DE-588)4020236-7 gnd Klassische Gruppe (DE-588)4164040-8 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4164040-8 |
| title | The geometry of the classical groups |
| title_auth | The geometry of the classical groups |
| title_exact_search | The geometry of the classical groups |
| title_full | The geometry of the classical groups Donald E. Taylor |
| title_fullStr | The geometry of the classical groups Donald E. Taylor |
| title_full_unstemmed | The geometry of the classical groups Donald E. Taylor |
| title_short | The geometry of the classical groups |
| title_sort | the geometry of the classical groups |
| topic | Correspondance Klein Jussieu Couple BN Jussieu Groupe A7 Jussieu Groupe Coxeter Jussieu Groupe Suzuki Jussieu Groupe Weyl Jussieu Groupe orthogonal Jussieu Groupe symplectique Jussieu Groupe unitaire Jussieu Groupes, théorie des ram Géométrie affine Jussieu Géométrie algébrique ram Géométrie groupe classique Jussieu Géométrie projective Jussieu Immeuble Tits Jussieu Théorème Witt Jussieu Geometry, Algebraic Group theory Geometrie (DE-588)4020236-7 gnd Klassische Gruppe (DE-588)4164040-8 gnd |
| topic_facet | Correspondance Klein Couple BN Groupe A7 Groupe Coxeter Groupe Suzuki Groupe Weyl Groupe orthogonal Groupe symplectique Groupe unitaire Groupes, théorie des Géométrie affine Géométrie algébrique Géométrie groupe classique Géométrie projective Immeuble Tits Théorème Witt Geometry, Algebraic Group theory Geometrie Klassische Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=003489304&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000012120 |
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