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Hilbert's fifth problem and related topics / Terence Tao.

By: Tao, Terence.
Material type: TextTextSeries: Graduate studies in mathematics ; v 153.Publisher: Providence : American Mathematical Society, c2014Description: xiii, 338 p. ; 27 cm.ISBN: 9781470415648 (hbk : alk. paper).Subject(s): Lie groups | Lie algebras | Characteristic functionsDDC classification: 512.482
Contents:
1. Introduction -- 2. Lie groups, Lie algebras, and the Baker-Campbell-Hausdorff formula -- 3. Building Lie structure from representations and metrics -- 4. Haar measure, the Peter-Weyl theorem, and compact or abelian groups -- 5. Building metrics on groups, and the Gleason-Yamabe theorem -- 6. The structure of locally compact groups -- 7. Ultraproducts as a bridge between hard analysis and soft analysis -- 8. Models of ultra approximate groups -- 9. The microscopic structure of approximate groups -- 10. Applications of the structural theory of approximate groups -- 11. The Jordan-Schur theorem -- 12. Nilpotent groups and nilprogressions -- 13. Ado's theorem -- 14. Associativity of the Baker-Campbell-Hausdorff-Dynkin law -- 15. Local groups -- 16. Central extensions of Lie groups, and cocycle averaging -- 17. The Hilbert-Smith conjecture -- 18. The Peter-Weyl theorem and nonabelian Fourier analysis -- 19. Polynomial bounds via nonstandard analysis -- 20. Loeb measure and the triangle removal lemma -- 21. Two notes on Lie groups-- Bibliography-- Index.
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Item type Current location Call number Status Date due Barcode Item holds
Books Books ISI Library, Kolkata
 
512.482 T171 (Browse shelf) Available 136354
Total holds: 0

Includes bibliographical references and index.

1. Introduction --
2. Lie groups, Lie algebras, and the Baker-Campbell-Hausdorff formula --
3. Building Lie structure from representations and metrics --
4. Haar measure, the Peter-Weyl theorem, and compact or abelian groups --
5. Building metrics on groups, and the Gleason-Yamabe theorem --
6. The structure of locally compact groups --
7. Ultraproducts as a bridge between hard analysis and soft analysis --
8. Models of ultra approximate groups --
9. The microscopic structure of approximate groups --
10. Applications of the structural theory of approximate groups --
11. The Jordan-Schur theorem --
12. Nilpotent groups and nilprogressions --
13. Ado's theorem --
14. Associativity of the Baker-Campbell-Hausdorff-Dynkin law --
15. Local groups --
16. Central extensions of Lie groups, and cocycle averaging --
17. The Hilbert-Smith conjecture --
18. The Peter-Weyl theorem and nonabelian Fourier analysis --
19. Polynomial bounds via nonstandard analysis --
20. Loeb measure and the triangle removal lemma --
21. Two notes on Lie groups--
Bibliography--
Index.

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