Kazhdan's property (T):
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge Univ. Press
2008
|
| Ausgabe: | 1. publ. |
| Schriftenreihe: | New mathematical monographs
11 |
| Schlagworte: | |
| Online-Zugang: | Table of contents only Inhaltsverzeichnis |
| Beschreibung: | Includes bibliographical references and index |
| Beschreibung: | XIII, 472 S. |
| ISBN: | 9780521887205 0521887208 |
Internformat
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| 245 | 1 | 0 | |a Kazhdan's property (T) |c Bachir Bekka ; Pierre de la Harpe ; Alain Valette |
| 250 | |a 1. publ. | ||
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| 500 | |a Includes bibliographical references and index | ||
| 600 | 1 | 4 | |a Kazhdan, D |
| 650 | 4 | |a Group theory | |
| 650 | 4 | |a Mathematics | |
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Datensatz im Suchindex
| _version_ | 1804138362183876608 |
|---|---|
| adam_text | KAZHDAN S PROPERTY (T) BACHIR BEKKA, PIERRE DE LA HARPE AND ALAIN
VALETTE CAMBRIDGE UNIVERSITY PRESS CONTENTS LIST OF FIGURES PAGE IX LIST
OF SYMBOLS ( X INTRODUCTION 1 HISTORICAL INTRODUCTION 4 PART I:
KAZHDAN S PROPERTY (T) 25 1 DEFINITIONS, FIRST CONSEQUENCES, AND BASIC
EXAMPLES 27 1.1 FIRST DEFINITION OF PROPERTY (T) 27 1.2 PROPERTY (T) IN
TERMS OF FELL S TOPOLOGY 32 1.3 COMPACT GENERATION AND OTHER
CONSEQUENCES 36 1.4 PROPERTY (T) FOR SLN (K), N 3 40 1.5 PROPERTY (T)
FOR SP 2N (K), N 2 50 1.6 PROPERTY (T) FOR HIGHER RANK ALGEBRAIC
GROUPS 58 1.7 HEREDITARY PROPERTIES 60 1.8 EXERCISES 67 2 PROPERTY (FH)
73 2.1 AFFINE ISOMETRIC ACTIONS AND PROPERTY (FH) 74 2.2 1-COHOMOLOGY 75
2.3 ACTIONS ON TREES 80 2.4 CONSEQUENCES OF PROPERTY (FH) 85 2.5
HEREDITARY PROPERTIES 88 2.6 ACTIONS ON REAL HYPERBOLIC SPACES 93 2.7
ACTIONS ON BOUNDARIES OF RANK 1 SYMMETRIC SPACES 100 2.8 WREATH PRODUCTS
104 2.9 ACTIONS ON THE CIRCLE 107 2.10 FUNCTIONS CONDITIONALLY OF
NEGATIVE TYPE 119 VI CONTENTS 2.11 A CONSEQUENCE OF SCHOENBERG S THEOREM
122 2.12 THE DELORME-GUICHARDET THEOREM 127 2.13 CONCORDANCE 132 2.14
EXERCISES 133 3 REDUCED COHOMOLOGY 136 3.1 AFFINE ISOMETRIC ACTIONS
ALMOST HAVING FIXED POINTS 137 3.2 A THEOREM BY Y. SHALOM 140 3.3
PROPERTY (T) FOR SP(N, 1) 151 3.4 THE QUESTION OF FINITE PRESENTABILITY
171 3.5 OTHER CONSEQUENCES OF SHALOM S THEOREM 175 3.6 PROPERTY (T) IS
NOT GEOMETRIC 179 3.7 EXERCISES { 182 4 BOUNDED GENERATION 184 4.1
BOUNDED GENERATION OF SL N (Z) FOR N 3 184 4.2 A KAZHDAN CONSTANT FOR
SL N (Z) 193 4.3 PROPERTY (T) FOR SLN(R) . 201 4.4 EXERCISES 213 5 A
SPECTRAL CRITERION FOR PROPERTY (T) 216 5.1 STATIONARY MEASURES FOR
RANDOM WALKS 217 5.2 LAPLACE AND MARKOV OPERATORS 218 5.3 RANDOM WALKS
ON FINITE SETS 222 5.4 G-EQUIVARIANT RANDOM WALKS ON QUASI-TRANSITIVE
FREE SETS 224 5.5 A LOCAL SPECTRAL CRITERION 236 5.6 ZUK S CRITERION 241
5.7 GROUPS ACTING ON A2-BUILDINGS 245 5.8 EXERCISES 250 6 SOME
APPLICATIONS OF PROPERTY (T) 253 6.1 EXPANDER GRAPHS 253 6.2 NORM OF
CONVOLUTION OPERATORS 262 6.3 ERGODIC THEORY AND PROPERTY (T) 264 6.4
UNIQUENESS OF INVARIANT MEANS 276 6.5 EXERCISES 279 7 A SHORT LIST OF
OPEN QUESTIONS 282 VI CONTENTS 2.11 A CONSEQUENCE OF SCHOENBERG S
THEOREM 122 2.12 THE DELORME-GUICHARDET THEOREM 127 2.13 CONCORDANCE 132
2.14 EXERCISES 133 REDUCED COHOMOLOGY 136 3.1 AFFINE ISOMETRIC ACTIONS
ALMOST HAVING 4 5 6 FIXED POINTS 3.2 A THEOREM BY Y. SHALOM 3.3 PROPERTY
(T) FOR SP(N, 1) 3.4 THE QUESTION OF FINITE PRESENTABILITY 3.5 OTHER
CONSEQUENCES OF SHALOM S THEOREM 3.6 PROPERTY (T) IS NOT GEOMETRIC 3.7
EXERCISES BOUNDED GENERATION 4.1 BOUNDED GENERATION OF SL N (Z) FOR N
3 4.2 A KAZHDAN CONSTANT FOR SL N (Z) 4.3 PROPERTY (T) FOR SL N (R) 4.4
EXERCISES A SPECTRAL CRITERION FOR PROPERTY (T) 5.1 STATIONARY MEASURES
FOR RANDOM WALKS 5.2 LAPLACE AND MARKOV OPERATORS 5.3 RANDOM WALKS ON
FINITE SETS 5.4 G-EQUIVARIANT RANDOM WALKS ON QUASI-TRANSITIVE FREE SETS
5.5 A LOCAL SPECTRAL CRITERION 5.6 ZUK S CRITERION 5.7 GROUPS ACTING ON
A2-BUILDINGS 5.8 EXERCISES SOME APPLICATIONS OF PROPERTY (T) 6.1
EXPANDER GRAPHS 6.2 NORM OF CONVOLUTION OPERATORS 6.3 ERGODIC THEORY AND
PROPERTY (T) 6.4 UNIQUENESS OF INVARIANT MEANS 6.5 EXERCISES 137 140 151
171 175 179 182 184 184 193 201 213 216 217 218 222 224 236 241 245 250
253 253 262 264 276 279 A SHORT LIST OF OPEN QUESTIONS 282 CONTENTS VII
PART II: BACKGROUND ON UNITARY REPRESENTATIONS 287 UNITARY GROUP
REPRESENTATIONS 289 A. 1 UNITARY REPRESENTATIONS 289 A.2 SCHUR S LEMMA
296 A.3 THE HAAR MEASURE OF A LOCALLY COMPACT GROUP 299 A.4 THE REGULAR
REPRESENTATION OF A LOCALLY COMPACT GROUP 305 A.5 REPRESENTATIONS OF
COMPACT GROUPS 306 A.6 UNITARY REPRESENTATIONS ASSOCIATED TO GROUP
ACTIONS 307 A.7 GROUP ACTIONS ASSOCIATED TO ORTHOGONAL REPRESENTATIONS
311 A.8 EXERCISES 321 MEASURES ON HOMOGENEOUS SPACES 324 B.I INVARIANT
MEASURES 324 B.2 LATTICES IN LOCALLY COMPACT GROUPS 332 B.3 EXERCISES
337 FUNCTIONS OF POSITIVE TYPE AND GNS CONSTRUCTION 340 C. 1 KERNELS OF
POSITIVE TYPE 340 345 349 351 357 365 C.2 C.3 C.4 C.5 C.6 KERNELS
CONDITIONALLY OF NEGATIVE TYPE SCHOENBERG S THEOREM FUNCTIONS ON GROUPS
THE CONE OF FUNCTIONS OF POSITIVE TYPE EXERCISES UNITARY REPRESENTATIONS
OF LOCALLY COMPACT D.I D.2 D.3 D.4 D.5 ABELIAN GROUPS THE FOURIER
TRANSFORM BOCHNER S THEOREM UNITARY REPRESENTATIONS OF LOCALLY COMPACT
ABELIAN GROUPS LOCAL FIELDS EXERCISES 369 369 372 373 377 380 E INDUCED
REPRESENTATIONS 383 E. 1 DEFINITION OF INDUCED REPRESENTATIONS 383 E.2
SOME PROPERTIES OF INDUCED REPRESENTATIONS 389 E.3 INDUCED
REPRESENTATIONS WITH INVARIANT VECTORS 391 E.4 EXERCISES 393 VIII
CONTENTS WEAK CONTAINMENT AND FELL S TOPOLOGY 395 F. 1 WEAK CONTAINMENT
OF UNITARY REPRESENTATIONS 395 F.2 FELL TOPOLOGY ON SETS OF UNITARY
REPRESENTATIONS 402 F.3 CONTINUITY OF OPERATIONS 407 F.4 THE C*
-ALGEBRAS OF A LOCALLY COMPACT GROUP 411 F.5 DIRECT INTEGRALS OF UNITARY
REPRESENTATIONS 413 F.6 EXERCISES 417 AMENABILITY 420 G.1 INVARIANT
MEANS 421 G2 EXAMPLES OF AMENABLE GROUPS 424 G.3 WEAK CONTAINMENT AND
AMENABILITY 427 G.4 KESTEN S CHARACTERISATION OF AMENABILITY 433 G.5
F0LNER S PROPERTY 440 G.6 EXERCISES 445 BIBLIOGRAPHY 449 INDEX 468
|
| adam_txt |
KAZHDAN'S PROPERTY (T) BACHIR BEKKA, PIERRE DE LA HARPE AND ALAIN
VALETTE CAMBRIDGE UNIVERSITY PRESS CONTENTS LIST OF FIGURES PAGE IX LIST
OF SYMBOLS ( X INTRODUCTION 1 HISTORICAL INTRODUCTION 4 PART I:
KAZHDAN'S PROPERTY (T) 25 1 DEFINITIONS, FIRST CONSEQUENCES, AND BASIC
EXAMPLES 27 1.1 FIRST DEFINITION OF PROPERTY (T) 27 1.2 PROPERTY (T) IN
TERMS OF FELL'S TOPOLOGY 32 1.3 COMPACT GENERATION AND OTHER
CONSEQUENCES 36 1.4 PROPERTY (T) FOR SLN (K), N 3 40 1.5 PROPERTY (T)
FOR SP 2N (K), N 2 50 1.6 PROPERTY (T) FOR HIGHER RANK ALGEBRAIC
GROUPS 58 1.7 HEREDITARY PROPERTIES 60 1.8 EXERCISES 67 2 PROPERTY (FH)
73 2.1 AFFINE ISOMETRIC ACTIONS AND PROPERTY (FH) 74 2.2 1-COHOMOLOGY 75
2.3 ACTIONS ON TREES 80 2.4 CONSEQUENCES OF PROPERTY (FH) 85 2.5
HEREDITARY PROPERTIES 88 2.6 ACTIONS ON REAL HYPERBOLIC SPACES 93 2.7
ACTIONS ON BOUNDARIES OF RANK 1 SYMMETRIC SPACES 100 2.8 WREATH PRODUCTS
104 2.9 ACTIONS ON THE CIRCLE 107 2.10 FUNCTIONS CONDITIONALLY OF
NEGATIVE TYPE 119 VI CONTENTS 2.11 A CONSEQUENCE OF SCHOENBERG'S THEOREM
122 2.12 THE DELORME-GUICHARDET THEOREM 127 2.13 CONCORDANCE 132 2.14
EXERCISES 133 3 REDUCED COHOMOLOGY 136 3.1 AFFINE ISOMETRIC ACTIONS
ALMOST HAVING FIXED POINTS 137 3.2 A THEOREM BY Y. SHALOM 140 3.3
PROPERTY (T) FOR SP(N, 1) 151 3.4 THE QUESTION OF FINITE PRESENTABILITY
171 3.5 OTHER CONSEQUENCES OF SHALOM'S THEOREM 175 3.6 PROPERTY (T) IS
NOT GEOMETRIC 179 3.7 EXERCISES { 182 4 BOUNDED GENERATION 184 4.1
BOUNDED GENERATION OF SL N (Z) FOR N 3 184 4.2 A KAZHDAN CONSTANT FOR
SL N (Z) 193 4.3 PROPERTY (T) FOR SLN(R) . 201 4.4 EXERCISES 213 5 A
SPECTRAL CRITERION FOR PROPERTY (T) 216 5.1 STATIONARY MEASURES FOR
RANDOM WALKS 217 5.2 LAPLACE AND MARKOV OPERATORS 218 5.3 RANDOM WALKS
ON FINITE SETS 222 5.4 G-EQUIVARIANT RANDOM WALKS ON QUASI-TRANSITIVE
FREE SETS 224 5.5 A LOCAL SPECTRAL CRITERION 236 5.6 ZUK'S CRITERION 241
5.7 GROUPS ACTING ON A2-BUILDINGS 245 5.8 EXERCISES 250 6 SOME
APPLICATIONS OF PROPERTY (T) 253 6.1 EXPANDER GRAPHS 253 6.2 NORM OF
CONVOLUTION OPERATORS 262 6.3 ERGODIC THEORY AND PROPERTY (T) 264 6.4
UNIQUENESS OF INVARIANT MEANS 276 6.5 EXERCISES 279 7 A SHORT LIST OF
OPEN QUESTIONS 282 VI CONTENTS 2.11 A CONSEQUENCE OF SCHOENBERG'S
THEOREM 122 2.12 THE DELORME-GUICHARDET THEOREM 127 2.13 CONCORDANCE 132
2.14 EXERCISES 133 REDUCED COHOMOLOGY 136 3.1 AFFINE ISOMETRIC ACTIONS
ALMOST HAVING 4 5 6 FIXED POINTS 3.2 A THEOREM BY Y. SHALOM 3.3 PROPERTY
(T) FOR SP(N, 1) 3.4 THE QUESTION OF FINITE PRESENTABILITY 3.5 OTHER
CONSEQUENCES OF SHALOM'S THEOREM 3.6 PROPERTY (T) IS NOT GEOMETRIC 3.7
EXERCISES BOUNDED GENERATION 4.1 BOUNDED GENERATION OF SL N (Z) FOR N
3 4.2 A KAZHDAN CONSTANT FOR SL N (Z) 4.3 PROPERTY (T) FOR SL N (R) 4.4
EXERCISES A SPECTRAL CRITERION FOR PROPERTY (T) 5.1 STATIONARY MEASURES
FOR RANDOM WALKS 5.2 LAPLACE AND MARKOV OPERATORS 5.3 RANDOM WALKS ON
FINITE SETS 5.4 G-EQUIVARIANT RANDOM WALKS ON QUASI-TRANSITIVE FREE SETS
5.5 A LOCAL SPECTRAL CRITERION 5.6 ZUK'S CRITERION 5.7 GROUPS ACTING ON
A2-BUILDINGS 5.8 EXERCISES SOME APPLICATIONS OF PROPERTY (T) 6.1
EXPANDER GRAPHS 6.2 NORM OF CONVOLUTION OPERATORS 6.3 ERGODIC THEORY AND
PROPERTY (T) 6.4 UNIQUENESS OF INVARIANT MEANS 6.5 EXERCISES 137 140 151
171 175 179 182 184 184 193 201 213 216 217 218 222 224 236 241 245 250
253 253 262 264 276 279 A SHORT LIST OF OPEN QUESTIONS 282 CONTENTS VII
PART II: BACKGROUND ON UNITARY REPRESENTATIONS 287 UNITARY GROUP
REPRESENTATIONS 289 A. 1 UNITARY REPRESENTATIONS 289 A.2 SCHUR'S LEMMA
296 A.3 THE HAAR MEASURE OF A LOCALLY COMPACT GROUP 299 A.4 THE REGULAR
REPRESENTATION OF A LOCALLY COMPACT GROUP 305 A.5 REPRESENTATIONS OF
COMPACT GROUPS 306 A.6 UNITARY REPRESENTATIONS ASSOCIATED TO GROUP
ACTIONS 307 A.7 GROUP ACTIONS ASSOCIATED TO ORTHOGONAL REPRESENTATIONS
311 A.8 EXERCISES 321 MEASURES ON HOMOGENEOUS SPACES 324 B.I INVARIANT
MEASURES 324 B.2 LATTICES IN LOCALLY COMPACT GROUPS 332 B.3 EXERCISES
337 FUNCTIONS OF POSITIVE TYPE AND GNS CONSTRUCTION 340 C. 1 KERNELS OF
POSITIVE TYPE 340 345 349 351 357 365 C.2 C.3 C.4 C.5 C.6 KERNELS
CONDITIONALLY OF NEGATIVE TYPE SCHOENBERG'S THEOREM FUNCTIONS ON GROUPS
THE CONE OF FUNCTIONS OF POSITIVE TYPE EXERCISES UNITARY REPRESENTATIONS
OF LOCALLY COMPACT D.I D.2 D.3 D.4 D.5 ABELIAN GROUPS THE FOURIER
TRANSFORM BOCHNER'S THEOREM UNITARY REPRESENTATIONS OF LOCALLY COMPACT
ABELIAN GROUPS LOCAL FIELDS EXERCISES 369 369 372 373 377 380 E INDUCED
REPRESENTATIONS 383 E. 1 DEFINITION OF INDUCED REPRESENTATIONS 383 E.2
SOME PROPERTIES OF INDUCED REPRESENTATIONS 389 E.3 INDUCED
REPRESENTATIONS WITH INVARIANT VECTORS 391 E.4 EXERCISES 393 VIII
CONTENTS WEAK CONTAINMENT AND FELL'S TOPOLOGY 395 F. 1 WEAK CONTAINMENT
OF UNITARY REPRESENTATIONS 395 F.2 FELL TOPOLOGY ON SETS OF UNITARY
REPRESENTATIONS 402 F.3 CONTINUITY OF OPERATIONS 407 F.4 THE C*
-ALGEBRAS OF A LOCALLY COMPACT GROUP 411 F.5 DIRECT INTEGRALS OF UNITARY
REPRESENTATIONS 413 F.6 EXERCISES 417 AMENABILITY 420 G.1 INVARIANT
MEANS 421 G2 EXAMPLES OF AMENABLE GROUPS 424 G.3 WEAK CONTAINMENT AND
AMENABILITY 427 G.4 KESTEN'S CHARACTERISATION OF AMENABILITY 433 G.5
F0LNER'S PROPERTY 440 G.6 EXERCISES 445 BIBLIOGRAPHY 449 INDEX 468 |
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| author | Bekka, Mohammed El Bachir |
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| author_facet | Bekka, Mohammed El Bachir |
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| author_sort | Bekka, Mohammed El Bachir |
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| bvnumber | BV035186342 |
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| dewey-full | 512.55 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.55 |
| dewey-search | 512.55 |
| dewey-sort | 3512.55 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| edition | 1. publ. |
| format | Book |
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| id | DE-604.BV035186342 |
| illustrated | Not Illustrated |
| index_date | 2024-07-02T22:59:52Z |
| indexdate | 2024-07-09T21:26:59Z |
| institution | BVB |
| isbn | 9780521887205 0521887208 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016993021 |
| oclc_num | 488573691 |
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| physical | XIII, 472 S. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Cambridge Univ. Press |
| record_format | marc |
| series | New mathematical monographs |
| series2 | New mathematical monographs |
| spelling | Bekka, Mohammed El Bachir Verfasser (DE-588)112010725 aut Kazhdan's property (T) Bachir Bekka ; Pierre de la Harpe ; Alain Valette 1. publ. Cambridge Cambridge Univ. Press 2008 XIII, 472 S. txt rdacontent n rdamedia nc rdacarrier New mathematical monographs 11 Includes bibliographical references and index Kazhdan, D Group theory Mathematics Topological groups Mathematik Topologische Gruppe (DE-588)4135793-0 gnd rswk-swf Topologische Gruppe (DE-588)4135793-0 s DE-604 La Harpe, Pierre de Sonstige (DE-588)108064158 oth Valette, Alain 1958- Sonstige (DE-588)143430378 oth New mathematical monographs 11 (DE-604)BV035420183 11 http://www.loc.gov/catdir/toc/fy0805/2008276469.html Table of contents only GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016993021&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Bekka, Mohammed El Bachir Kazhdan's property (T) New mathematical monographs Kazhdan, D Group theory Mathematics Topological groups Mathematik Topologische Gruppe (DE-588)4135793-0 gnd |
| subject_GND | (DE-588)4135793-0 |
| title | Kazhdan's property (T) |
| title_auth | Kazhdan's property (T) |
| title_exact_search | Kazhdan's property (T) |
| title_exact_search_txtP | Kazhdan's property (T) |
| title_full | Kazhdan's property (T) Bachir Bekka ; Pierre de la Harpe ; Alain Valette |
| title_fullStr | Kazhdan's property (T) Bachir Bekka ; Pierre de la Harpe ; Alain Valette |
| title_full_unstemmed | Kazhdan's property (T) Bachir Bekka ; Pierre de la Harpe ; Alain Valette |
| title_short | Kazhdan's property (T) |
| title_sort | kazhdan s property t |
| topic | Kazhdan, D Group theory Mathematics Topological groups Mathematik Topologische Gruppe (DE-588)4135793-0 gnd |
| topic_facet | Kazhdan, D Group theory Mathematics Topological groups Mathematik Topologische Gruppe |
| url | http://www.loc.gov/catdir/toc/fy0805/2008276469.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016993021&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV035420183 |
| work_keys_str_mv | AT bekkamohammedelbachir kazhdanspropertyt AT laharpepierrede kazhdanspropertyt AT valettealain kazhdanspropertyt |