Compositions of Quadratic Forms

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Walter de Gruyter, 2000 - Mathematics - 417 pages
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The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, 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 interested in a thorough study of the subject.

Editorial Board

Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil
Walter D. Neumann, Columbia University, New York, USA
Markus J. Pflaum, University of Colorado, Boulder, USA
Dierk Schleicher, Jacobs University, Bremen, Germany
Katrin Wendland, University of Freiburg, Germany

Honorary Editor

Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia

Titles in planning include

Yuri A. Bahturin, Identical Relations in Lie Algebras (2019)
Yakov G. Berkovich and Z. Janko, Groups of Prime Power Order, Volume 6 (2019)
Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019)
Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019)
Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021)
Ioannis Diamantis, Bostjan Gabrovsek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

 

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Contents

Exercises
5
Chapter
13
Appendix Composition algebras
21
Notes
36
Exercises
46
Chapter 3
52
Exercises
64
Notes
71
Notes
175
Exercises
196
Notes
202
Appendix Hasse principle for divisibility of forms
218
Introduction
227
Appendix More applications of topology to algebra
252
Notes
264
Integer Composition Formulas
268

Appendix A Hermitian forms over C
81
Notes
89
Exercises
101
Chapter 6
108
Exercises
116
Exercises
131
Exercises
150
Notes
157
Appendix Pfister forms and function fields
167
Appendix A A new proof of Yuzvinskys theorem
286
Chapter 14
299
Appendix Compositions of quadratic forms a J y
317
Appendix Polynomial maps between spheres
348
Notes
361
Exercises
375
List of Symbols
407
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