Ergodic theory and semisimple groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Boston [u.a.]
Birkhäuser
1984
|
| Schriftenreihe: | Monographs in mathematics
81 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | X, 209 S. |
| ISBN: | 0817631844 3764331844 |
Internformat
MARC
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Datensatz im Suchindex
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|---|---|
| adam_text | Table of Contents
Preface ix
1. Introduction 1
1.1. Statement of some main results 1
1.2. Outline of the succeeding chapters 5
2. Moore s Ergodicity Theorem 8
2.1. Ergodicity and smoothness 8
2.2. Moore s theorem: statement and some consequences ... 17
2.3. Unitary representations of semi direct products, I .... 23
2.4. Vanishing of matrix coefficients for semisimple groups . . 28
3. Algebraic Groups and Measure Theory 32
3.1. Review of algebraic groups 32
3.2. Orbits of measures on projective varieties and the Borel density
theorem 38
3.3. Orbits in function spaces 49
3.4. Rationality of measurable mappings first results.... 52
3.5. A homomorphism theorem 56
4. Amenability 59
4.1. Amenable groups 59
4.2. Cocycles 65
4.3. Amenable actions . 77
5. Rigidity 85
5.1. Margulis superrigidity theorem and the Mostow Margulis
rigidity theorem 85
5.2. Rigidity and orbit equivalence of ergodic actions .... 95
6. Margulis Arithmeticity Theorems 114
6.1. Arithmeticity in groups of real rank at least 2 114
6.2. The commensurability criterion 122
7. Kazhdan s Property (T) 130
7.1. Kazhdan s property and some consequences 130
7.2. Amenability and unitary representations 133
7.3. Unitary representations of semi direct products, II . . .139
7.4. Kazhdan s property for semisimple groups 146
viii Contents
8. Normal Subgroups of Lattices 149
8.1. Margulis finiteness theorem statement and first steps of
proof 149
8.2. Contracting automorphisms of groups 152
8.3. Completion of the proof equivariant measurable quotients of
flag varieties 157
9. Further Results on Ergodic Actions 162
9.1. Cocycles and Kazhdan s property 162
9.2. The algebraic hull of a cocycle 166
9.3. Actions of lattices and product actions 169
9.4. Rigidity and entropy 175
9.5. Complements 183
10. Generalizations to p adic groups and S arithmetic groups . . .187
Appendices 194
A. Borel spaces 194
B. Almost everywhere identities on groups 197
References 202
Subject Index 208
|
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| illustrated | Not Illustrated |
| indexdate | 2024-07-09T15:11:41Z |
| institution | BVB |
| isbn | 0817631844 3764331844 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-000173774 |
| oclc_num | 10824326 |
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| physical | X, 209 S. |
| publishDate | 1984 |
| publishDateSearch | 1984 |
| publishDateSort | 1984 |
| publisher | Birkhäuser |
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| series | Monographs in mathematics |
| series2 | Monographs in mathematics |
| spelling | Zimmer, Robert J. Verfasser aut Ergodic theory and semisimple groups Robert J. Zimmer Boston [u.a.] Birkhäuser 1984 X, 209 S. txt rdacontent n rdamedia nc rdacarrier Monographs in mathematics 81 Ergodiciteit gtt Lie-groepen gtt Ergodic theory Semisimple Lie groups Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 gnd rswk-swf Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd rswk-swf Ergodentheorie (DE-588)4015246-7 s Halbeinfache Lie-Gruppe (DE-588)4122188-6 s DE-604 Lie-Gruppe (DE-588)4035695-4 s Monographs in mathematics 81 (DE-604)BV000008284 81 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000173774&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Zimmer, Robert J. Ergodic theory and semisimple groups Monographs in mathematics Ergodiciteit gtt Lie-groepen gtt Ergodic theory Semisimple Lie groups Lie-Gruppe (DE-588)4035695-4 gnd Ergodentheorie (DE-588)4015246-7 gnd Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd |
| subject_GND | (DE-588)4035695-4 (DE-588)4015246-7 (DE-588)4122188-6 |
| title | Ergodic theory and semisimple groups |
| title_auth | Ergodic theory and semisimple groups |
| title_exact_search | Ergodic theory and semisimple groups |
| title_full | Ergodic theory and semisimple groups Robert J. Zimmer |
| title_fullStr | Ergodic theory and semisimple groups Robert J. Zimmer |
| title_full_unstemmed | Ergodic theory and semisimple groups Robert J. Zimmer |
| title_short | Ergodic theory and semisimple groups |
| title_sort | ergodic theory and semisimple groups |
| topic | Ergodiciteit gtt Lie-groepen gtt Ergodic theory Semisimple Lie groups Lie-Gruppe (DE-588)4035695-4 gnd Ergodentheorie (DE-588)4015246-7 gnd Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd |
| topic_facet | Ergodiciteit Lie-groepen Ergodic theory Semisimple Lie groups Lie-Gruppe Ergodentheorie Halbeinfache Lie-Gruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=000173774&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000008284 |
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