Compositions of Quadratic Forms ( De Gruyter Expositions in Mathematics )

Publication series ：De Gruyter Expositions in Mathematics

Author： Daniel B. Shapiro  

Publisher： De Gruyter‎

Publication year： 2000

E-ISBN: 9783110824834

P-ISBN(Paperback): 9783110126297

Subject： O156.5 quadratic (quadratic)

Language： ENG

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Description

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics.

The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic.

Editorial Board

Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil
Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany

Chapter

Introduction

pp.：  1 – 11

Chapter 0. Historical Background

pp.：  11 – 15

Exercises

pp.：  15 – 19

Notes

pp.：  19 – 23

Part I. Classical Compositions and Quadratic Forms

pp.：  23 – 25

Chapter 1. Spaces of Similarities

pp.：  25 – 27

Appendix. Composition algebras

pp.：  27 – 35

Exercises

pp.：  35 – 39

Notes

pp.：  39 – 50

Chapter 2. Amicable Similarities

pp.：  50 – 53

Exercises

pp.：  53 – 60

Notes

pp.：  60 – 65

Chapter 3. Clifford Algebras

pp.：  65 – 66

Exercises

pp.：  66 – 78

Notes

pp.：  78 – 85

Chapter 4. C-Modules and the Decomposition Theorem

pp.：  85 – 87

Appendix. λ-Hermitian forms over C

pp.：  87 – 95

Exercises

pp.：  95 – 97

Notes

pp.：  97 – 103

Chapter 5. Small (s, t)-Families

pp.：  103 – 104

Exercises

pp.：  104 – 115

Notes

pp.：  115 – 120

Chapter 6. Involutions

pp.：  120 – 122

Exercises

pp.：  122 – 130

Notes

pp.：  130 – 132

Chapter 7. Unsplittable (σ, τ)-Modules

pp.：  132 – 133

Exercises

pp.：  133 – 145

Notes

pp.：  145 – 148

Chapter 8. The Space of All Compositions

pp.：  148 – 149

Exercises

pp.：  149 – 164

Notes

pp.：  164 – 171

Chapter 9. The Pfister Factor Conjecture

pp.：  171 – 174

Appendix. Pfister forms and function fields

pp.：  174 – 181

Exercises

pp.：  181 – 184

Notes

pp.：  184 – 189

Chapter 10. Central Simple Algebras and an Expansion Theorem

pp.：  189 – 190

Exercises

pp.：  190 – 210

Notes

pp.：  210 – 216

Chapter 11. Hasse Principles

pp.：  216 – 218

Appendix. Hasse principle for divisibility of forms

pp.：  218 – 232

Exercises

pp.：  232 – 234

Notes

pp.：  234 – 237

Part II. Compositions of Size [r, s, n]

pp.：  237 – 239

Introduction

pp.：  239 – 241

Chapter 12. [r, s, n]-Formulas and Topology

pp.：  241 – 245

Appendix. More applications of topology to algebra

pp.：  245 – 266

Exercises

pp.：  266 – 270

Notes

pp.：  270 – 278

Chapter 13. Integer Composition Formulas

pp.：  278 – 282

Appendix A. A new proof of Yuzvinsky’s theorem

pp.：  282 – 300

Appendix B. Monomial compositions

pp.：  300 – 302

Appendix C. Known upper bounds for r * s

pp.：  302 – 305

Exercises

pp.：  305 – 308

Notes

pp.：  308 – 311

Chapter 14. Compositions over General Fields

pp.：  311 – 313

Appendix. Compositions of quadratic forms α, β, γ

pp.：  313 – 331

Exercises

pp.：  331 – 335

Notes

pp.：  335 – 341

Chapter 15. Hopf Constructions and Hidden Formulas

pp.：  341 – 343

Appendix. Polynomial maps between spheres

pp.：  343 – 362

Exercises

pp.：  362 – 367

Notes

pp.：  367 – 375

Chapter 16. Related Topics

pp.：  375 – 377

B. Vector products and composition algebras

pp.：  377 – 382

A. Higher degree forms permitting composition

pp.：  377 – 377

C. Compositions over rings and over fields of characteristic 2

pp.：  382 – 384

D. Linear spaces of matrices of constant rank

pp.：  384 – 386

Exercises

pp.：  386 – 389

Notes

pp.：  389 – 394

References

pp.：  394 – 395

List of Symbols

pp.：  395 – 421

Index

pp.：  421 – 427

LastPages

pp.：  427 – 433

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