Octonions, Jordan algebras, and exceptional groups:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English German |
| Published: |
Berlin [u.a.]
Springer
2000
|
| Series: | Springer Monographs in mathematics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | VIII, 208 S. |
| ISBN: | 3540663371 |
Staff View
MARC
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| 245 | 1 | 0 | |a Octonions, Jordan algebras, and exceptional groups |c Tonny A. Springer ; Ferdinand D. Veldkamp |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2000 | |
| 300 | |a VIII, 208 S. | ||
| 336 | |b txt |2 rdacontent | ||
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| 650 | 4 | |a Linear algebraic groups | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
1. Composition Algebras 1
1.1 Quadratic and Bilinear Forms 1
1.2 Composition Algebras. The Minimum Equation 4
1.3 Conjugation. Inverses 7
1.4 Moufang Identities. Alternative Laws 9
1.5 Subalgebras. Doubling 11
1.6 Structure and Dimension of a Composition Algebra 14
1.7 A Composition Algebra is Determined by its Norm 16
1.8 Split Composition Algebras 18
1.9 Center and Associating Elements 20
1.10 Classification over Special Fields 21
1.11 Historical Notes 23
2. The Automorphism Group of an Octonion Algebra 25
2.1 Automorphisms Leaving a Quaternion Subalgebra Invariant.. 25
2.2 Connectedness and Dimension of the Automorphism Group .. 26
2.3 The Automorphism Group is of Type G2 30
2.4 Derivations and the Lie Algebra of the Automorphism Group 33
2.5 Historical Notes 35
3. Triality 37
3.1 Similarities. Clifford Algebras, Spin Groups and Spinor Norms 37
3.2 The Principle of Triality 42
3.3 Outer Automorphisms Defined by Triality 45
3.4 Automorphism Group and Rotation Group of an Octonion
Algebra 48
3.5 Local Triality 50
3.6 The Spin Group of an Octonion Algebra 58
3.7 Fields of Definition 65
3.8 Historical Notes 66
4. Twisted Composition Algebras 69
4.1 Normal Twisted Composition Algebras 70
4.2 Nonnormal Twisted Composition Algebras 79
4.3 Twisted Composition Algebras over Split Cubic Extensions .. 89
VIII Contents
4.4 Automorphism Groups of Twisted Octonion Algebras 92
4.5 Normal Twisted Octonion Algebras with Isotropic Norm .... 94
4.6 A Construction of Isotropic Normal Twisted Octonion Algebras 99
4.7 A Related Central Simple Associative Algebra 102
4.8 A Criterion for Reduced Twisted Octonion Algebras. Appli¬
cations 105
4.9 More on Isotropic Normal Twisted Octonion Algebras 108
4.10 Nonnormal Twisted Octonion Algebras with Isotropic Norm . 110
4.11 Twisted Composition Algebras with Anisotropic Norm 112
4.12 Historical Notes 115
5. J algebras and Albert Algebras 117
5.1 J algebras. Definition and Basic Properties 117
5.2 Cross Product. Idempotents 122
5.3 Reduced J algebras and Their Decomposition 125
5.4 Classification of Reduced J algebras 133
5.5 Further Properties of Reduced J algebras 141
5.6 Uniqueness of the Composition Algebra 145
5.7 Norm Class of a Primitive Idempotent 149
5.8 Isomorphism Criterion. Classification over Some Fields 152
5.9 Isotopes. Orbits of the Invariance Group of the Determinant . 154
5.10 Historical Notes 159
6. Proper J algebras and Twisted Composition Algebras .... 161
6.1 Reducing Fields of J algebras 161
6.2 From J algebras to Twisted Composition Algebras 163
6.3 From Twisted Composition Algebras to J algebras 167
6.4 Historical Notes 171
7. Exceptional Groups 173
7.1 The Automorphisms Fixing a Given Primitive Idempotent... 173
7.2 The Automorphism Group of an Albert Algebra 178
7.3 The Invariance Group of the Determinant in an
Albert Algebra 180
7.4 Historical Notes 182
8. Cohomological Invariants 185
8.1 Galois Cohomology 185
8.2 An Invariant of Composition Algebras 189
8.3 An Invariant of Twisted Octonion Algebras 191
8.4 An Invariant of Albert Algebras 195
8.5 The Freudenthal Tits Construction 199
8.6 Historical Notes 200
References 201
Index 205
|
| any_adam_object | 1 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| id | DE-604.BV012980000 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:37:09Z |
| institution | BVB |
| isbn | 3540663371 |
| language | English German |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-008843568 |
| oclc_num | 43317927 |
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| physical | VIII, 208 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer Monographs in mathematics |
| spelling | Springer, Tonny A. 1926- Verfasser (DE-588)115799729 aut Octonions, Jordan algebras, and exceptional groups Tonny A. Springer ; Ferdinand D. Veldkamp Berlin [u.a.] Springer 2000 VIII, 208 S. txt rdacontent n rdamedia nc rdacarrier Springer Monographs in mathematics Algebraïsche groepen gtt Anneaux alternatifs Anneaux alternatifs ram Groupes algébriques linéaires ram Groupes linéaires algébriques Jordan, Algèbres de Jordan, Algèbres de ram Jordan-algebra's gtt Ringen (wiskunde) gtt Alternative rings Cayley numbers Jordan algebras Linear algebraic groups Ausnahmegruppe (DE-588)4221271-6 gnd rswk-swf Oktave Mathematik (DE-588)4595894-4 gnd rswk-swf Jordan-Algebra (DE-588)4162770-2 gnd rswk-swf Oktave Mathematik (DE-588)4595894-4 s Jordan-Algebra (DE-588)4162770-2 s Ausnahmegruppe (DE-588)4221271-6 s DE-604 Veldkamp, Ferdinand D. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008843568&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Springer, Tonny A. 1926- Veldkamp, Ferdinand D. Octonions, Jordan algebras, and exceptional groups Algebraïsche groepen gtt Anneaux alternatifs Anneaux alternatifs ram Groupes algébriques linéaires ram Groupes linéaires algébriques Jordan, Algèbres de Jordan, Algèbres de ram Jordan-algebra's gtt Ringen (wiskunde) gtt Alternative rings Cayley numbers Jordan algebras Linear algebraic groups Ausnahmegruppe (DE-588)4221271-6 gnd Oktave Mathematik (DE-588)4595894-4 gnd Jordan-Algebra (DE-588)4162770-2 gnd |
| subject_GND | (DE-588)4221271-6 (DE-588)4595894-4 (DE-588)4162770-2 |
| title | Octonions, Jordan algebras, and exceptional groups |
| title_auth | Octonions, Jordan algebras, and exceptional groups |
| title_exact_search | Octonions, Jordan algebras, and exceptional groups |
| title_full | Octonions, Jordan algebras, and exceptional groups Tonny A. Springer ; Ferdinand D. Veldkamp |
| title_fullStr | Octonions, Jordan algebras, and exceptional groups Tonny A. Springer ; Ferdinand D. Veldkamp |
| title_full_unstemmed | Octonions, Jordan algebras, and exceptional groups Tonny A. Springer ; Ferdinand D. Veldkamp |
| title_short | Octonions, Jordan algebras, and exceptional groups |
| title_sort | octonions jordan algebras and exceptional groups |
| topic | Algebraïsche groepen gtt Anneaux alternatifs Anneaux alternatifs ram Groupes algébriques linéaires ram Groupes linéaires algébriques Jordan, Algèbres de Jordan, Algèbres de ram Jordan-algebra's gtt Ringen (wiskunde) gtt Alternative rings Cayley numbers Jordan algebras Linear algebraic groups Ausnahmegruppe (DE-588)4221271-6 gnd Oktave Mathematik (DE-588)4595894-4 gnd Jordan-Algebra (DE-588)4162770-2 gnd |
| topic_facet | Algebraïsche groepen Anneaux alternatifs Groupes algébriques linéaires Groupes linéaires algébriques Jordan, Algèbres de Jordan-algebra's Ringen (wiskunde) Alternative rings Cayley numbers Jordan algebras Linear algebraic groups Ausnahmegruppe Oktave Mathematik Jordan-Algebra |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=008843568&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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