Spinors and calibrations:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston u.a.
Academic Pr.
1990
|
| Schriftenreihe: | Perspectives in mathematics
9 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XIII, 323 S. |
| ISBN: | 0123296501 |
Internformat
MARC
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| 100 | 1 | |a Harvey, F. R. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Spinors and calibrations |c F. Reese Harvey |
| 264 | 1 | |a Boston u.a. |b Academic Pr. |c 1990 | |
| 300 | |a XIII, 323 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
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| 490 | 1 | |a Perspectives in mathematics |v 9 | |
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Datensatz im Suchindex
| _version_ | 1804118059783290880 |
|---|---|
| adam_text | TABLE OF CONTENTS
PREFACE xi
PART I: CLASSICAL GROUPS AND NORMED ALGEBRAS
1. CLASSICAL GROUPS I 3
The General Linear Groups 4
Groups Defined by Bilinear Forms 6
Other Miscellaneous Groups 8
Isomorphisms 13
Summary 15
2. THE EIGHT TYPES OF INNER PRODUCT SPACES .... 19
The Standard Models 22
Orthogonality 23
A Canonical Form (The Basis Theorem) 29
The Parts of an Inner Product 31
3. CLASSICAL GROUPS II 41
Group Representations and Orbits 41
Generalized Spheres 42
The Basis Theorem Revisited 46
Adjoints 47
Lie Algebras 48
4. EUCLIDEAN/LORENTZIAN VECTORS SPACES 57
The Cauchy Schwarz Equality 58
Special Relativity 62
The Cartan Dieudonne Theorem 67
Grassmannians and SO*(p, q), the Reduced Special
Orthogonal Groups 75
5. DIFFERENTIAL GEOMETRY 81
Real n Manifolds: The Group GL(n, R) 81
Oriented Real n Manifolds: The Group GL+(n,R) 82
Complex (and Almost Complex) n Manifolds:
The Group GL(n, C) 83
Quaternionic (and Almost Quaternionic) n Manifolds:
The Group GL(n,H)H* 85
Manifolds with Volume: The Groups SL(n, R) and SL(n, C) . . 86
Riemannian Manifolds (of Signature p, q): The Group O(p, q) . 87
Conformal Manifolds (of Signature p, q): The Group CO(p, q) . 87
vii
viii Table of Contents
5. DIFFERENTIAL GEOMETRY (continued)
Real Symplectic Manifolds: The Group Sp(n, R) 87
Complex Riemannian Manifolds: The Group O(n, C) 88
Complex Symplectic Manifolds: The Group Sp(n, C) 88
Kahler Manifolds (of Signature p,q): The Group U(p,q) .... 89
Special Kahler Manifolds (of Signature p, q): The Group SU(p, q) 90
HyperKahler Manifolds (of Signature p, q): The Group HU(p, q) 91
Quaternionic Kahler Manifolds (of Signature p, q):
The Group EXJ(p,q) • HU(1) 92
Quaternionic Skew Hermitian Manifolds:
The Group SK(n, H) 93
Coincidences of Geometries in Low Dimensions 94
6. NORMED ALGEBRAS 101
The Cayley Dickson Process 104
The Hurwitz Theorem 107
Cross Products 110
The Exceptional Lie Group G2 113
7. CALIBRATIONS 125
The Fundamental Theorem 125
The Kahler Case 127
The Special Lagrangian Calibration 130
The Special Lagrangian Differential Equation 134
Examples of Special Lagrangian Submanifolds 138
Associative Geometry 144
The Angle Theorem 146
Generalized Nance Calibrations and Complex Structures . . 156
8. MATRIX ALGEBRAS 163
Representations 163
Uniqueness of Intertwining Operators 167
Automorphisms 169
Inner Products 170
PART II: SPINORS
9. THE CLIFFORD ALGEBRAS 177
The Clifford Automorphisms 181
The Clifford Involutions 182
The Clifford Inner Product 184
Spinors and Calibrations ix
9. THE CLIFFORD ALGEBRAS (continued)
The Main Symmetry 185
The Clifford Center 187
Self Duality 188
Trace 189
The Complex Clifford Algebras 190
10. THE GROUPS SPIN AND PIN 195
The Grassmannians and Reflections 197
Additional Groups for Nondefinite Signature 199
The Conformal Pin (or Clifford) Group 201
Determinants 203
11. THE CLIFFORD ALGEBRAS Cl(r,s) AS ALGEBRAS . ... 207
The Pinor Representations 210
The Spinor Representations 213
The First Proof 215
The Spinor Structure Map on P(r, s) 217
Even Dimensions 217
Odd Dimensions 220
12. THE SPLIT CASE Cl(p,p) 227
A Model for Cl(p,p) 227
Pinor Inner Products for Cl(p,p)^ EndR(P(p,p)) 230
The Complex Clifford Algebras
(Continued from Chapter 9) 233
Cl(r, s)(r + s = 2p) as a Subalgebra of
Clc(2p) = Cl(p,p)®R.C 235
The Pinor Reality Map 237
A Second Proof of the Classification Theorem 240
Pure Spinors 241
13. INNER PRODUCTS ON THE SPACES OF SPINORS
AND PINORS 247
The Spinor Inner Product 247
The Spin Representation and the (Reduced) Classical
Companion Group Cp°(r,s) 250
The Pinor Inner Products € and i 252
Pinor Multiplication 266
Signature 268
x Table of Contents
14. LOW DIMENSIONS 271
Cartan s Isomorphisms 271
Triality 275
Transitive Actions on Spheres 283
The Cayley Plane and the Exceptional Group F4 289
Clifford Algebras in Low Dimensions 298
Squares of Spinors and Calibrations 308
REFERENCES 315
INDEX 317
|
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| id | DE-604.BV003714910 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T16:04:17Z |
| institution | BVB |
| isbn | 0123296501 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002364677 |
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| physical | XIII, 323 S. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
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| series | Perspectives in mathematics |
| series2 | Perspectives in mathematics |
| spelling | Harvey, F. R. Verfasser aut Spinors and calibrations F. Reese Harvey Boston u.a. Academic Pr. 1990 XIII, 323 S. txt rdacontent n rdamedia nc rdacarrier Perspectives in mathematics 9 Matrix groups Spinor analysis Spinor (DE-588)4182327-8 gnd rswk-swf Spinoranalysis (DE-588)4182329-1 gnd rswk-swf Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Matrizengruppe (DE-588)4169127-1 gnd rswk-swf Spinoranalysis (DE-588)4182329-1 s DE-604 Matrizengruppe (DE-588)4169127-1 s Differentialgeometrie (DE-588)4012248-7 s Spinor (DE-588)4182327-8 s Perspectives in mathematics 9 (DE-604)BV000770492 9 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002364677&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Harvey, F. R. Spinors and calibrations Perspectives in mathematics Matrix groups Spinor analysis Spinor (DE-588)4182327-8 gnd Spinoranalysis (DE-588)4182329-1 gnd Differentialgeometrie (DE-588)4012248-7 gnd Matrizengruppe (DE-588)4169127-1 gnd |
| subject_GND | (DE-588)4182327-8 (DE-588)4182329-1 (DE-588)4012248-7 (DE-588)4169127-1 |
| title | Spinors and calibrations |
| title_auth | Spinors and calibrations |
| title_exact_search | Spinors and calibrations |
| title_full | Spinors and calibrations F. Reese Harvey |
| title_fullStr | Spinors and calibrations F. Reese Harvey |
| title_full_unstemmed | Spinors and calibrations F. Reese Harvey |
| title_short | Spinors and calibrations |
| title_sort | spinors and calibrations |
| topic | Matrix groups Spinor analysis Spinor (DE-588)4182327-8 gnd Spinoranalysis (DE-588)4182329-1 gnd Differentialgeometrie (DE-588)4012248-7 gnd Matrizengruppe (DE-588)4169127-1 gnd |
| topic_facet | Matrix groups Spinor analysis Spinor Spinoranalysis Differentialgeometrie Matrizengruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002364677&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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