Discrete subgroups of semisimple Lie groups:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
1991
|
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
3. Folge ; 17 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | Aus d. Russ. übers. |
| Physical Description: | IX, 388 S. |
| ISBN: | 354012179X 038712179X |
Staff View
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| 100 | 1 | |a Margulis, Grigorij A. |d 1946- |e Verfasser |0 (DE-588)128622881 |4 aut | |
| 245 | 1 | 0 | |a Discrete subgroups of semisimple Lie groups |c G. A. Margulis |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 1991 | |
| 300 | |a IX, 388 S. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge |v 17 | |
| 500 | |a Aus d. Russ. übers. | ||
| 650 | 4 | |a Groupes de Lie semi-simples | |
| 650 | 7 | |a Lie, groupes de, semisimples |2 ram | |
| 650 | 4 | |a Treillis, Théorie des | |
| 650 | 7 | |a Treillis, théorie des |2 ram | |
| 650 | 4 | |a Lattice theory | |
| 650 | 4 | |a Semisimple Lie groups | |
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Record in the Search Index
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| adam_text | Table of Contents
Introduction 1
1. Statement of Main Results 1
2. Synopsis of the Chapters 5
3. Remarks on the Structure of the Book, References and Notation 7
Chapter I. Preliminaries 8
0. Notation, Terminology and Some Basic Facts 8
1. Algebraic Groups Over Arbitrary Fields 37
2. Algebraic Groups Over Local Fields 49
3. Arithmetic Groups 59
4. Measure Theory and Ergodic Theory 66
5. Unitary Representations and Amenable Groups 72
Chapter II. Density and Ergodicity Theorems 79
1. Iterations of Linear Transformations 80
2. Density Theorems for Subgroups with Property (S)I 83
3. The Generalized Mautner Lemma and the Lebesgue Spectrum 85
4. Density Theorems for Subgroups with Property (S)II 92
5. Non Discrete Closed Subgroups of Finite Covolume 95
6. Density of Projections and the Strong Approximation Theorem 99
7. Ergodicity of Actions on Quotient Spaces 105
Chapter III. Property (T) 107
1. Representations Which Are Isolated from the
Trivial One Dimensional Representation 108
2. Property (T) and Some of Its Consequences. Relationship Between
Property (T) for Groups and for Their Subgroups 114
3. Property (T) and Decompositions of Groups into Amalgams 119
4. Property (R) 125
5. Semisimple Groups with Property (T) 129
6. Relationship Between the Structure of Closed Subgroups
and Property (T) of Normal Subgroups 137
viii Table of Contents
Chapter IV. Factor Groups of Discrete Subgroups 145
1. b metrics, Vitali s Covering Theorem and the
Density Point Theorem 145
2. Invariant Algebras of Measurable Sets 150
3. Amenable Factor Groups of Lattices Lying in Direct Products 155
4. Finiteness of Factor Groups of Discrete Subgroups 163
Chapter V. Characteristic Maps 168
1. Auxiliary Assertions 168
2. The Multiplicative Ergodic Theorem 170
3. Definition and Fundamental Properties of Characteristic Maps 174
4. Effective Pairs 180
5. Essential Pairs 186
Chapter VI. Discrete Subgroups and Boundary Theory 195
1. Proximal G Spaces and Boundaries 195
2. // Boundaries 198
3. Projective G Spaces 203
4. Equivariant Measurable Maps to Algebraic Varieties 207
Chapter VII. Rigidity 214
1. Auxiliary Assertions 214
2. Cocycles on G Spaces 216
3. Finite Dimensional Invariant Subspaces 217
4. Equivariant Measurable Maps and Continuous Extensions
of Representations 220
5. Superrigidity (Continuous Extensions of Homomorphisms
of Discrete Subgroups to Algebraic Groups Over Local Fields) 224
6. Homomorphisms of Discrete Subgroups to Algebraic Groups
Over Arbitrary Fields 243
7. Strong Rigidity (Continuous Extensions of Isomorphisms
of Discrete Subgroups) 251
8. Rigidity of Ergodic Actions of Semisimple Groups 254
Chapter VIII. Normal Subgroups and Abstract Homomorphisms
of Semisimple Algebraic Groups Over Global Fields 258
1. Some Properties of Fundamental Domains
for S Arithmetic Subgroups 260
2. Finiteness of Factor Groups of S Arithmetic Subgroups 263
3. Homomorphisms of S Arithmetic Subgroups to Algebraic Groups 271
Chapter IX. Arithmeticity 288
1. Statement of the Arithmeticity Theorems 288
2. Proof of the Arithmeticity Theorems 299
Table of Contents ix
3. Finite Generation of Lattices 311
4. Consequences of the Arithmeticity Theorems I 315
5. Consequences of the Arithmeticity Theorems II 323
6. Arithmeticity, Volume of Quotient Spaces, Finiteness of Factor Groups,
and Superrigidity of Lattices in Semisimple Lie Groups 328
7. Applications to the Theory of Symmetric Spaces
and Theory of Complex Manifolds 334
Appendices 346
A. Proof of the Multiplicative Ergodic Theorem 346
B. Free Discrete Subgroups of Linear Groups 351
C. Examples of Non Arithmetic Lattices 353
Historical and Bibliographical Notes 369
References 372
Subject Index 386
|
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| indexdate | 2024-07-09T16:11:45Z |
| institution | BVB |
| isbn | 354012179X 038712179X |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-002700011 |
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| physical | IX, 388 S. |
| publishDate | 1991 |
| publishDateSearch | 1991 |
| publishDateSort | 1991 |
| publisher | Springer |
| record_format | marc |
| series | Ergebnisse der Mathematik und ihrer Grenzgebiete |
| series2 | Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge |
| spelling | Margulis, Grigorij A. 1946- Verfasser (DE-588)128622881 aut Discrete subgroups of semisimple Lie groups G. A. Margulis Berlin [u.a.] Springer 1991 IX, 388 S. txt rdacontent n rdamedia nc rdacarrier Ergebnisse der Mathematik und ihrer Grenzgebiete : 3. Folge 17 Aus d. Russ. übers. Groupes de Lie semi-simples Lie, groupes de, semisimples ram Treillis, Théorie des Treillis, théorie des ram Lattice theory Semisimple Lie groups Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd rswk-swf Lie-Gruppe (DE-588)4035695-4 gnd rswk-swf Diskrete Untergruppe (DE-588)4257236-8 gnd rswk-swf Halbeinfache Lie-Gruppe (DE-588)4122188-6 s Diskrete Untergruppe (DE-588)4257236-8 s DE-604 Lie-Gruppe (DE-588)4035695-4 s Ergebnisse der Mathematik und ihrer Grenzgebiete 3. Folge ; 17 (DE-604)BV000899194 17 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002700011&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Margulis, Grigorij A. 1946- Discrete subgroups of semisimple Lie groups Ergebnisse der Mathematik und ihrer Grenzgebiete Groupes de Lie semi-simples Lie, groupes de, semisimples ram Treillis, Théorie des Treillis, théorie des ram Lattice theory Semisimple Lie groups Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd Diskrete Untergruppe (DE-588)4257236-8 gnd |
| subject_GND | (DE-588)4122188-6 (DE-588)4035695-4 (DE-588)4257236-8 |
| title | Discrete subgroups of semisimple Lie groups |
| title_auth | Discrete subgroups of semisimple Lie groups |
| title_exact_search | Discrete subgroups of semisimple Lie groups |
| title_full | Discrete subgroups of semisimple Lie groups G. A. Margulis |
| title_fullStr | Discrete subgroups of semisimple Lie groups G. A. Margulis |
| title_full_unstemmed | Discrete subgroups of semisimple Lie groups G. A. Margulis |
| title_short | Discrete subgroups of semisimple Lie groups |
| title_sort | discrete subgroups of semisimple lie groups |
| topic | Groupes de Lie semi-simples Lie, groupes de, semisimples ram Treillis, Théorie des Treillis, théorie des ram Lattice theory Semisimple Lie groups Halbeinfache Lie-Gruppe (DE-588)4122188-6 gnd Lie-Gruppe (DE-588)4035695-4 gnd Diskrete Untergruppe (DE-588)4257236-8 gnd |
| topic_facet | Groupes de Lie semi-simples Lie, groupes de, semisimples Treillis, Théorie des Treillis, théorie des Lattice theory Semisimple Lie groups Halbeinfache Lie-Gruppe Lie-Gruppe Diskrete Untergruppe |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002700011&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000899194 |
| work_keys_str_mv | AT margulisgrigorija discretesubgroupsofsemisimpleliegroups |