Expansion in finite simple groups of Lie type:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Providence, Rhode Island
American Mathematical Society
[2015]
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| Schriftenreihe: | Graduate studies in mathematics
volume 164 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverzeichnis Seite 293-300 |
| Beschreibung: | xiii, 303 Seiten Diagramme (farbig) |
| ISBN: | 9781470421960 |
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| 650 | 7 | |a Group theory and generalizations ... Linear algebraic groups and related topics ... Linear algebraic groups over finite fields |2 msc | |
| 650 | 4 | |a Finite simple groups | |
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Datensatz im Suchindex
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| adam_text | Titel: Expansion in finite simple groups of Lie type
Autor: Tao, Terence
Jahr: 2015
Contents Preface Notation Acknowledgments Part 1. Expansion in Cayley Graphs Chapter 1. Expander graphs: Basic theory §1.1. Expander graphs §1.2. Connection with edge expansion §1.3. Random walks on expanders §1.4. Random graphs as expanders Chapter 2. Expansion in Cayley graphs, and Kazhdan’s property (T) §2.1. Kazhdan’s property (T) §2.2. Induced representations and property (T) §2.3. The special linear group and property (T) §2.4. A more elementary approach Chapter 3. Quasirandom groups §3.1. Mixing in quasirandom groups §3.2. An algebraic description of quasirandomness §3.3. A weak form of Selberg’s 3/16 theorem Chapter 4. The Balog-Szemerédi-Gowers lemma, and the Bourgain- Gamburd expansion machine §4.1. The Balog-Szemerédi-Gowers lemma xi xii xiii 3 4 9 15 17 23 27 37 47 55 57 62 67 67 85 87
Contents viii §4.2. The Bourgain-Gamburd expansion machine 97 Chapter 5. Product theorems, pivot arguments, and the Larsen-Pink nonconcentration inequality 101 §5.1. The sum-product theorem 104 §5.2. Finite subgroups of SL 2 110 §5.3. The product theorem in SL 2 (ft) 120 §5.4. The product theorem in SLd(fc) 125 §5.5. Proof of the Larsen-Pink inequality 129 Chapter 6. Nonconcentration in subgroups 135 §6.1. Expansion in thin subgroups 137 §6.2. Random generators expand 140 Chapter 7. Sieving and expanders 143 §7.1. Combinatorial sieving 146 §7.2. The strong approximation property 156 §7.3. Sieving in thin groups 160 Part 2. Related Articles Chapter 8. Cayley graphs and the algebra of groups 167 §8.1. A Hall-Witt identity for 2-cocycles 177 Chapter 9. The Lang-Weil bound 187 §9.1. The Stepanov-Bombieri proof of the Hasse-Weil bound 194 §9.2. The proof of the Lang-Weil bound 198 §9.3. Lang-Weil with parameters 200 Chapter 10. The spectral theorem and its converses for unbounded self-adjoint operators 203 §10.1. Self-adjointness and resolvents 207 §10.2. Self-adjointness and spectral measure 212 §10.3. Self-adjointness and flows 218 §10.4. Essential self-adjointness of the Laplace-Beltrami operator 224 Chapter 11. Notes on Lie algebras 227 §11.1. Abelian representations 233 §11.2. Engel’s theorem and Lie’s theorem 235 §11.3. Characterising semisimplicity 237 §11.4. Cartan subalgebras 242
Contents IX §11.5. s [2 representations 245 §11.6. Root spaces 247 §11.7. Classification of root systems 251 §11.8. Chevalley bases 258 §11.9. Casimirs and complete reducibility 263 Chapter 12. Notes on groups of Lie type 267 §12.1. Simple Lie groups over C 268 §12.2. Chevalley groups 278 §12.3. Finite simple groups of Lie type 288 Bibliography 293 Index 301
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| spelling | Tao, Terence 1975- Verfasser (DE-588)132190370 aut Expansion in finite simple groups of Lie type Terence Tao Providence, Rhode Island American Mathematical Society [2015] © 2015 xiii, 303 Seiten Diagramme (farbig) txt rdacontent n rdamedia nc rdacarrier Graduate studies in mathematics volume 164 Literaturverzeichnis Seite 293-300 Combinatorics ... Graph theory ... Random walks on graphs msc Number theory ... Sequences and sets ... Arithmetic combinatorics; higher degree uniformity msc Group theory and generalizations ... Representation theory of groups ... Representations of finite groups of Lie type msc Group theory and generalizations ... Abstract finite groups ... Simple groups: alternating groups and groups of Lie type msc Group theory and generalizations ... Linear algebraic groups and related topics ... Linear algebraic groups over finite fields msc Finite simple groups Lie groups Combinatorics ... Graph theory ... Random walks on graphs Number theory ... Sequences and sets ... Arithmetic combinatorics; higher degree uniformity Group theory and generalizations ... Representation theory of groups ... Representations of finite groups of Lie type Group theory and generalizations ... Abstract finite groups ... Simple groups: alternating groups and groups of Lie type Group theory and generalizations ... Linear algebraic groups and related topics ... Linear algebraic groups over finite fields Cayley-Graph (DE-588)4751330-5 gnd rswk-swf Einfache Lie-Gruppe (DE-588)4309130-1 gnd rswk-swf Endliche Lie-Gruppe (DE-588)4448040-4 gnd rswk-swf Endliche Lie-Gruppe (DE-588)4448040-4 s Einfache Lie-Gruppe (DE-588)4309130-1 s Cayley-Graph (DE-588)4751330-5 s DE-604 Erscheint auch als Online-Ausgabe 978-1-4704-2265-3 Graduate studies in mathematics volume 164 (DE-604)BV009739289 164 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028056374&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Tao, Terence 1975- Expansion in finite simple groups of Lie type Graduate studies in mathematics Combinatorics ... Graph theory ... Random walks on graphs msc Number theory ... Sequences and sets ... Arithmetic combinatorics; higher degree uniformity msc Group theory and generalizations ... Representation theory of groups ... Representations of finite groups of Lie type msc Group theory and generalizations ... Abstract finite groups ... Simple groups: alternating groups and groups of Lie type msc Group theory and generalizations ... Linear algebraic groups and related topics ... Linear algebraic groups over finite fields msc Finite simple groups Lie groups Combinatorics ... Graph theory ... Random walks on graphs Number theory ... Sequences and sets ... Arithmetic combinatorics; higher degree uniformity Group theory and generalizations ... Representation theory of groups ... Representations of finite groups of Lie type Group theory and generalizations ... Abstract finite groups ... Simple groups: alternating groups and groups of Lie type Group theory and generalizations ... Linear algebraic groups and related topics ... Linear algebraic groups over finite fields Cayley-Graph (DE-588)4751330-5 gnd Einfache Lie-Gruppe (DE-588)4309130-1 gnd Endliche Lie-Gruppe (DE-588)4448040-4 gnd |
| subject_GND | (DE-588)4751330-5 (DE-588)4309130-1 (DE-588)4448040-4 |
| title | Expansion in finite simple groups of Lie type |
| title_auth | Expansion in finite simple groups of Lie type |
| title_exact_search | Expansion in finite simple groups of Lie type |
| title_full | Expansion in finite simple groups of Lie type Terence Tao |
| title_fullStr | Expansion in finite simple groups of Lie type Terence Tao |
| title_full_unstemmed | Expansion in finite simple groups of Lie type Terence Tao |
| title_short | Expansion in finite simple groups of Lie type |
| title_sort | expansion in finite simple groups of lie type |
| topic | Combinatorics ... Graph theory ... Random walks on graphs msc Number theory ... Sequences and sets ... Arithmetic combinatorics; higher degree uniformity msc Group theory and generalizations ... Representation theory of groups ... Representations of finite groups of Lie type msc Group theory and generalizations ... Abstract finite groups ... Simple groups: alternating groups and groups of Lie type msc Group theory and generalizations ... Linear algebraic groups and related topics ... Linear algebraic groups over finite fields msc Finite simple groups Lie groups Combinatorics ... Graph theory ... Random walks on graphs Number theory ... Sequences and sets ... Arithmetic combinatorics; higher degree uniformity Group theory and generalizations ... Representation theory of groups ... Representations of finite groups of Lie type Group theory and generalizations ... Abstract finite groups ... Simple groups: alternating groups and groups of Lie type Group theory and generalizations ... Linear algebraic groups and related topics ... Linear algebraic groups over finite fields Cayley-Graph (DE-588)4751330-5 gnd Einfache Lie-Gruppe (DE-588)4309130-1 gnd Endliche Lie-Gruppe (DE-588)4448040-4 gnd |
| topic_facet | Combinatorics ... Graph theory ... Random walks on graphs Number theory ... Sequences and sets ... Arithmetic combinatorics; higher degree uniformity Group theory and generalizations ... Representation theory of groups ... Representations of finite groups of Lie type Group theory and generalizations ... Abstract finite groups ... Simple groups: alternating groups and groups of Lie type Group theory and generalizations ... Linear algebraic groups and related topics ... Linear algebraic groups over finite fields Finite simple groups Lie groups Cayley-Graph Einfache Lie-Gruppe Endliche Lie-Gruppe |
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