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Hilbert’s Fifth Problem and Related Topics
About this Title
Terence Tao, University of California, Los Angeles, CA
Publication: Graduate Studies in Mathematics
Publication Year:
2014; Volume 153
ISBNs: 978-1-4704-1564-8 (print); 978-1-4704-1856-4 (online)
DOI: https://doi.org/10.1090/gsm/153
MathSciNet review: MR3237440
MSC: Primary 22D05; Secondary 11B30, 20F65, 22E05
Table of Contents
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Front/Back Matter
Part 1. Hilbert’s Fifth Problem
- Chapter 1. Introduction
- Chapter 2. Lie groups, Lie algebras, and the Baker-Campbell-Hausdorff formula
- Chapter 3. Building Lie structure from representations and metrics
- Chapter 4. Haar measure, the Peter-Weyl theorem, and compact or abelian groups
- Chapter 5. Building metrics on groups, and the Gleason-Yamabe theorem
- Chapter 6. The structure of locally compact groups
- Chapter 7. Ultraproducts as a bridge between hard analysis and soft analysis
- Chapter 8. Models of ultra approximate groups
- Chapter 9. The microscopic structure of approximate groups
- Chapter 10. Applications of the structural theory of approximate groups
Part 2. Related articles
- Chapter 11. The Jordan-Schur theorem
- Chapter 12. Nilpotent groups and nilprogressions
- Chapter 13. Ado’s theorem
- Chapter 14. Associativity of the Baker-Campbell-Hausdorff-Dynkin law
- Chapter 15. Local groups
- Chapter 16. Central extensions of Lie groups, and cocycle averaging
- Chapter 17. The Hilbert-Smith conjecture
- Chapter 18. The Peter-Weyl theorem and nonabelian Fourier analysis
- Chapter 19. Polynomial bounds via nonstandard analysis
- Chapter 20. Loeb measure and the triangle removal lemma
- Chapter 21. Two notes on Lie groups