Compositions of Quadratic Forms
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Daniel B. Shapiro
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it has only appeared in research papers, but quite a few points have been streamlined, and some results were previously unpublished.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
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Frontmatter
I -
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Table of Contents
VII -
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Introduction
XI -
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Chapter 0 Historical Background
1 - Part I Classical Compositions and Quadratic Forms
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Chapter 1 Spaces of Similarities
13 -
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Chapter 2 Amicable Similarities
39 -
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Chapter 3 Clifford Algebras
52 -
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Chapter 4 C-Modules and the Decomposition Theorem
73 -
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Chapter 5 Small (s, t)-Families
90 -
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Chapter 6 Involutions
108 -
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Chapter 7 Unsplittable (σ, τ)-Modules
119 -
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Chapter 8 The Space of All Compositions
135 -
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Chapter 9 The Pfister Factor Conjecture
160 -
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Chapter 10 Central Simple Algebras and an Expansion Theorem
176 -
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Chapter 11 Hasse Principles
204 - Part II Compositions of Size [r, s, n]
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Introduction
227 -
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Chapter 12 [r, s, n]-Formulas and Topology
231 -
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Chapter 13 Integer Composition Formulas
268 -
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Chapter 14 Compositions over General Fields
299 -
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Chapter 15 Hopf Constructions and Hidden Formulas
329 -
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Chapter 16 Related Topics
363 -
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References
381 -
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List of Symbols
407 -
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Index
413
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