The role of nonassociative algebra in projective geometry:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Soc.
2014
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| Series: | Graduate studies in mathematics
159 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIV, 229 S. graph. Darst. |
| ISBN: | 9781470418496 |
Staff View
MARC
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Record in the Search Index
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| adam_text | Titel: The role of nonassociative algebra in projective geometry
Autor: Faulkner, John R
Jahr: 2014
Contents Introduction xi Chapter 1. Affine and Projective Planes 1 §1.1. Preview 1 §1.2. Incidence geometry 2 §1.3. Affine planes 3 §1.4. Projective planes 4 §1.5. Duality 8 §1.6. Exercises 10 Chapter 2. Central Automorphisms of Projective Planes 13 §2.1. Preview 13 §2.2. Projections and automorphisms 14 §2.3. Transvections and dilatations 14 §2.4. Transitivity properties 16 §2.5. Exercises 22 Chapter 3. Coordinates for Projective Planes 23 §3.1. Preview 23 §3.2. Ternary systems 24 §3.3. Two coordinatizations related to G{C) 31 §3.4. Transvections and algebraic properties 33 §3.5. Exercises 40 vii
Contents viii Chapter 4. Alternative Rings 43 §4.1. Preview 43 §4.2. Left Moufang rings 44 §4.3. Artin’s Theorem 47 §4.4. Inverses in alternative rings 49 §4.5. The Cayley-Dickson process 50 §4.6. Composition algebras 54 §4.7. Split and division composition algebras 57 §4.8. Exercises 62 Chapter 5. Configuration Conditions 65 §5.1. Preview 65 §5.2. Desargues condition 66 §5.3. Quadrangle sections 71 §5.4. Pappus condition 75 §5.5. Configurations and central automorphisms 78 §5.6. Exercises 84 Chapter 6. Dimension Theory 87 §6.1. Preview 87 §6.2. Dimensionable sets 88 §6.3. Independence and bases 90 §6.4. Strongly dimensionable sets 94 §6.5. Exercises 96 Chapter 7. Projective Geometries 99 §7.1. Preview 99 §7.2. Projective and nearly projective geometries 100 §7.3. Relation to strongly dimensionable sets 102 §7.4. Classification of projective geometries 104 §7.5. Exercises 112 Chapter 8. Automorphisms of G(V) 115 §8.1. Preview 115 §8.2. The Fundamental Theorem 116 §8.3. Subgroups of Aut( ?(C)) 118 §8.4. Simple groups 120 §8.5. Exercises 121
Contents ix Chapter 9. Quadratic Forms and Orthogonal Groups 123 §9.1. Preview 123 §9.2. Quadratic forms 124 §9.3. Orthogonal groups 126 §9.4. Exercises 129 Chapter 10. Homogeneous Maps 131 §10.1. Preview 131 §10.2. Polarization of homogeneous maps 132 §10.3. Exercises 140 Chapter 11. Norms and Hermitian Matrices 143 §11.1. Preview 143 §11.2. Hermitian matrices and HE„(C) 144 §11.3. Norms on 7i(C n ) 146 §11.4. Transitivity of HE„(C) 153 §11.5. Trace and adjoint 157 §11.6. n{C 3 ) 160 §11.7. Exercises 165 Chapter 12. Octonion Planes 169 §12.1. Preview 169 §12.2. The construction of octonion planes 170 §12.3. Simplicity of PHE 3 (ö) 174 §12.4. Automorphisms of octonion planes 177 §12.5. Exercises 178 Chapter 13. Projective Remoteness Planes 181 §13.1. Preview 181 §13.2. Definition and examples 182 §13.3. Groups of Steinberg type 186 §13.4. Transvections 192 §13.5. Exercises 195 Chapter 14. Other Geometries 199 §14.1. Preview 199 §14.2. Erlangen program 200 §14.3. The geometry of i?-spaccs 201
X Contents §14.4. Buildings 206 §14.5. Generalized n-gons 209 §14.6. Moufang sets and structurable algebras 213 §14.7. Freudenthal-Tits magic square 214 §14.8. Exercises 218 Bibliography 221 Index 225
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| language | English |
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| publishDate | 2014 |
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| publisher | American Mathematical Soc. |
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| series | Graduate studies in mathematics |
| series2 | Graduate studies in mathematics |
| spelling | Faulkner, John R. 1943- Verfasser (DE-588)1071724614 aut The role of nonassociative algebra in projective geometry John R. Faulkner Providence, RI American Mathematical Soc. 2014 XIV, 229 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics 159 Geometry Linear incidence geometry Algebraization Ring geometry Nonassociative rings and algebras Projektive Geometrie (DE-588)4047436-7 gnd rswk-swf Nichtassoziative Algebra (DE-588)4297760-5 gnd rswk-swf Projektive Geometrie (DE-588)4047436-7 s Nichtassoziative Algebra (DE-588)4297760-5 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-1933-2 Graduate studies in mathematics 159 (DE-604)BV009739289 159 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027590999&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Faulkner, John R. 1943- The role of nonassociative algebra in projective geometry Graduate studies in mathematics Geometry Linear incidence geometry Algebraization Ring geometry Nonassociative rings and algebras Projektive Geometrie (DE-588)4047436-7 gnd Nichtassoziative Algebra (DE-588)4297760-5 gnd |
| subject_GND | (DE-588)4047436-7 (DE-588)4297760-5 |
| title | The role of nonassociative algebra in projective geometry |
| title_auth | The role of nonassociative algebra in projective geometry |
| title_exact_search | The role of nonassociative algebra in projective geometry |
| title_full | The role of nonassociative algebra in projective geometry John R. Faulkner |
| title_fullStr | The role of nonassociative algebra in projective geometry John R. Faulkner |
| title_full_unstemmed | The role of nonassociative algebra in projective geometry John R. Faulkner |
| title_short | The role of nonassociative algebra in projective geometry |
| title_sort | the role of nonassociative algebra in projective geometry |
| topic | Geometry Linear incidence geometry Algebraization Ring geometry Nonassociative rings and algebras Projektive Geometrie (DE-588)4047436-7 gnd Nichtassoziative Algebra (DE-588)4297760-5 gnd |
| topic_facet | Geometry Linear incidence geometry Algebraization Ring geometry Nonassociative rings and algebras Projektive Geometrie Nichtassoziative Algebra |
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