Compositions of quadratic forms:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; New York
<<de>> Gruyter
2000
|
| Series: | De Gruyter expositions in mathematics
33 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII, 417 S. |
| ISBN: | 311012629X |
Staff View
MARC
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Record in the Search Index
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|---|---|
| adam_text | Table of Contents
Introduction xi
Chapter 0
Historical Background 1
Exercises 5
Notes 9
Part I. Classical Compositions and Quadratic Forms
Chapter 1
Spaces of Similarities 13
Appendix. Composition algebras 21
Exercises 25
Notes 36
Chapter 2
Amicable Similarities 39
Exercises 46
Notes 51
Chapter 3
Clifford Algebras 52
Exercises 64
Notes 71
Chapter 4
C Modules and the Decomposition Theorem 73
Appendix. A Hermitian forms over C 81
Exercises 83
Notes 89
Chapter 5
Small (s, O Families 90
Exercises 101
Notes 106
viii Table of Contents
Chapter 6
Involutions 108
Exercises 116
Notes 118
Chapter 7
Unsplittable (a, r) Modules 119
Exercises 131
Notes 134
Chapter 8
The Space of All Compositions 135
Exercises 150
Notes 157
Chapter 9
The Pfister Factor Conjecture 160
Appendix. Pfister forms and function fields 167
Exercises 170
Notes 175
Chapter 10
Central Simple Algebras and an Expansion Theorem 176
Exercises 196
Notes 202
Chapter 11
Hasse Principles 204
Appendix. Hasse principle for divisibility of forms 218
Exercises 220
Notes 223
Part II. Compositions of Size [r, s, n]
Introduction 227
Chapter 12
[r,s, n] Formulas and Topology 231
Appendix. More applications of topology to algebra 252
Exercises 256
Notes 264
Table of Contents ix
Chapter 13
Integer Composition Formulas 268
Appendix A. A new proof of Yuzvinsky s theorem 286
Appendix B. Monomial compositions 288
Appendix C. Known upper bounds for r * s 291
Exercises 294
Notes 297
Chapter 14
Compositions over General Fields 299
Appendix. Compositions of quadratic forms a, p, y 317
Exercises 321
Notes 327
Chapter 15
Hopf Constructions and Hidden Formulas 329
Appendix. Polynomial maps between spheres 348
Exercises 353
Notes 361
Chapter 16
Related Topics 363
A. Higher degree forms permitting composition 363
B. Vector products and composition algebras 368
C. Compositions over rings and over fields of characteristic 2 370
D. Linear spaces of matrices of constant rank 372
Exercises 375
Notes 380
References 381
List of Symbols 407
Index 413
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T18:43:02Z |
| institution | BVB |
| isbn | 311012629X |
| language | English |
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| physical | XIII, 417 S. |
| publishDate | 2000 |
| publishDateSearch | 2000 |
| publishDateSort | 2000 |
| publisher | <<de>> Gruyter |
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| series | De Gruyter expositions in mathematics |
| series2 | De Gruyter expositions in mathematics |
| spelling | Shapiro, Daniel B. Verfasser aut Compositions of quadratic forms by Daniel B. Shapiro Berlin ; New York <<de>> Gruyter 2000 XIII, 417 S. txt rdacontent n rdamedia nc rdacarrier De Gruyter expositions in mathematics 33 Formes quadratiques ram Forms, Quadratic Quadratische Form (DE-588)4128297-8 gnd rswk-swf Quadratische Form (DE-588)4128297-8 s DE-604 De Gruyter expositions in mathematics 33 (DE-604)BV004069300 33 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=009054224&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Shapiro, Daniel B. Compositions of quadratic forms De Gruyter expositions in mathematics Formes quadratiques ram Forms, Quadratic Quadratische Form (DE-588)4128297-8 gnd |
| subject_GND | (DE-588)4128297-8 |
| title | Compositions of quadratic forms |
| title_auth | Compositions of quadratic forms |
| title_exact_search | Compositions of quadratic forms |
| title_full | Compositions of quadratic forms by Daniel B. Shapiro |
| title_fullStr | Compositions of quadratic forms by Daniel B. Shapiro |
| title_full_unstemmed | Compositions of quadratic forms by Daniel B. Shapiro |
| title_short | Compositions of quadratic forms |
| title_sort | compositions of quadratic forms |
| topic | Formes quadratiques ram Forms, Quadratic Quadratische Form (DE-588)4128297-8 gnd |
| topic_facet | Formes quadratiques Forms, Quadratic Quadratische Form |
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