Compositions of Quadratic Forms

Daniel B. Shapiro

Published by De Gruyter 2000

Compositions of Quadratic Forms

Daniel B. Shapiro

Volume 33 in the series De Gruyter Expositions in Mathematics

https://doi.org/10.1515/9783110824834

Overview
Contents

Reviews

"This is an introduction to the field, a research monograph, and a comprehensive survey."
P. Schmitt, Wien, in: Monatshefte für Mathematik, Wien, 1/2003

"[…] the book under review contains an impressive wealth of material. Most of it has only appeared in research papers, but quite a few points have been streamlined, and some results were previously unpublished. The mathematical taste of the author also contributes to this abundance: he obviously takes pleasure (to the reader's delight) in discussing topics which are marginally related to compositions of quadratic forms if they look striking or particularly appealing in some ways." Mathematical Reviews

"The author considers all facets, variations and generalisations of this theme in great detail. Many different ideas and methods from algebra, geometry, combinatorics and topology have been used and are presented here. The choice of material shows good taste and reveals the author’s love for this subject. A lot of exercises and 25 pages of references to the original literature complete the book." Zentralblatt für Mathematik

Topics

Frontmatter Requires Authentication Unlicensed Licensed Download PDF	I
Table of Contents Requires Authentication Unlicensed Licensed Download PDF	VII
Introduction Requires Authentication Unlicensed Licensed Download PDF	XI
Chapter 0 Historical Background Requires Authentication Unlicensed Licensed Download PDF	1
Part I Classical Compositions and Quadratic Forms
Chapter 1 Spaces of Similarities Requires Authentication Unlicensed Licensed Download PDF	13
Chapter 2 Amicable Similarities Requires Authentication Unlicensed Licensed Download PDF	39
Chapter 3 Clifford Algebras Requires Authentication Unlicensed Licensed Download PDF	52
Chapter 4 C-Modules and the Decomposition Theorem Requires Authentication Unlicensed Licensed Download PDF	73
Chapter 5 Small (s, t)-Families Requires Authentication Unlicensed Licensed Download PDF	90
Chapter 6 Involutions Requires Authentication Unlicensed Licensed Download PDF	108
Chapter 7 Unsplittable (σ, τ)-Modules Requires Authentication Unlicensed Licensed Download PDF	119
Chapter 8 The Space of All Compositions Requires Authentication Unlicensed Licensed Download PDF	135
Chapter 9 The Pfister Factor Conjecture Requires Authentication Unlicensed Licensed Download PDF	160
Chapter 10 Central Simple Algebras and an Expansion Theorem Requires Authentication Unlicensed Licensed Download PDF	176
Chapter 11 Hasse Principles Requires Authentication Unlicensed Licensed Download PDF	204
Part II Compositions of Size [r, s, n]
Introduction Requires Authentication Unlicensed Licensed Download PDF	227
Chapter 12 [r, s, n]-Formulas and Topology Requires Authentication Unlicensed Licensed Download PDF	231
Chapter 13 Integer Composition Formulas Requires Authentication Unlicensed Licensed Download PDF	268
Chapter 14 Compositions over General Fields Requires Authentication Unlicensed Licensed Download PDF	299
Chapter 15 Hopf Constructions and Hidden Formulas Requires Authentication Unlicensed Licensed Download PDF	329
Chapter 16 Related Topics Requires Authentication Unlicensed Licensed Download PDF	363
References Requires Authentication Unlicensed Licensed Download PDF	381
List of Symbols Requires Authentication Unlicensed Licensed Download PDF	407
Index Requires Authentication Unlicensed Licensed Download PDF	413

Language: English
Publisher: De Gruyter
Edition: Reprint 2011
Pages
- Front matter: 13
- Main content: 417
Keywords: Quadratische Form

eBook

Published: June 24, 2011
ISBN: 9783110824834

Hardcover

Published: August 31, 2000
ISBN: 9783110126297