Compositions of quadratic forms /
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| Author / Creator: | Shapiro, Daniel B., 1948- |
|---|---|
| Imprint: | Berlin ; New York : Walter de Gruyter, 2000. |
| Description: | xiii, 417 p. 25 cm. |
| Language: | English |
| Series: | De Gruyter expositions in mathematics 0938-6572 ; 33 |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/4386275 |
Table of Contents:
- Introduction
- Chapter 0. Historical Background
- Exercises
- Notes
- Part I.. Classical Compositions and Quadratic Forms
- Chapter 1. Spaces of Similarities
- Appendix.. Composition algebras
- Exercises
- Notes
- Chapter 2. Amicable Similarities
- Exercises
- Notes
- Chapter 3. Clifford Algebras
- Exercises
- Notes
- Chapter 4. C-Modules and the Decomposition Theorem
- Appendix.. [lambda]-Hermitian forms over C
- Exercises
- Notes
- Chapter 5. Small (s, t)-Families
- Exercises
- Notes
- Chapter 6. Involutions
- Exercises
- Notes
- Chapter 7. Unsplittable ([sigma], [tau])-Modules
- Exercises
- Notes
- Chapter 8. The Space of All Compositions
- Exercises
- Notes
- Chapter 9. The Pfister Factor Conjecture
- Appendix.. Pfister forms and function fields
- Exercises
- Notes
- Chapter 10. Central Simple Algebras and an Expansion Theorem
- Exercises
- Notes
- Chapter 11. Hasse Principles
- Appendix.. Hasse principle for divisibility of forms
- Exercises
- Notes
- Part II.. Compositions of Size [r, s, n]
- Introduction
- Chapter 12. [r, s, n]-Formulas and Topology
- Appendix.. More applications of topology to algebra
- Exercises
- Notes
- Chapter 13. Integer Composition Formulas
- Appendix A.. A new proof of Yuzvinsky's theorem
- Appendix B.. Monomial compositions
- Appendix C.. Known upper bounds for r * s
- Exercises
- Notes
- Chapter 14. Compositions over General Fields
- Appendix.. Compositions of quadratic forms [alpha], [beta], [gamma]
- Exercises
- Notes
- Chapter 15. Hopf Constructions and Hidden Formulas
- Appendix.. Polynomial maps between spheres
- Exercises
- Notes
- Chapter 16. Related Topics
- A.. Higher degree forms permitting composition
- B.. Vector products and composition algebras
- C.. Compositions over rings and over fields of characteristic 2
- D.. Linear spaces of matrices of constant rank
- Exercises
- Notes
- References
- List of Symbols
- Index
