The structure of compact groups: a primer for the student ; a handbook for the expert
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Berlin [u.a.]
De Gruyter
2013
|
| Ausgabe: | 3. ed., revised and augmented |
| Schriftenreihe: | De Gruyter Studies in Mathematics
25 |
| Schlagworte: | |
| Online-Zugang: | Inhaltstext Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. [867] - 884 |
| Beschreibung: | XXII, 924 S. graph. Darst. 240 mm x 170 mm |
| ISBN: | 3110296551 9783110296556 9783110296808 |
Internformat
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| 245 | 1 | 0 | |a The structure of compact groups |b a primer for the student ; a handbook for the expert |c Karl H. Hofmann ; Sidney A. Morris |
| 250 | |a 3. ed., revised and augmented | ||
| 264 | 1 | |a Berlin [u.a.] |b De Gruyter |c 2013 | |
| 300 | |a XXII, 924 S. |b graph. Darst. |c 240 mm x 170 mm | ||
| 336 | |b txt |2 rdacontent | ||
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Datensatz im Suchindex
| _version_ | 1806325720610242560 |
|---|---|
| adam_text |
IMAGE 1
CONTENTS
CHAPTER 1. BASIC TOPICS AND EXAMPLES 1
DEFINITIONS AND ELEMENTARY EXAMPLES 2
ACTIONS, SUBGROUPS, QUOTIENT SPACES 5
PRODUCTS OF COMPACT GROUPS 10
APPLICATIONS TO ABELIAN GROUPS 11
PROJECTIVE LIMITS 17
TOTALLY DISCONNECTED COMPACT GROUPS 22
SOME DUALITY THEORY 24
POSTSCRIPT 29
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 30
CHAPTER 2. THE BASIC REPRESENTATION THEORY OF COMPACT GROUPS 31
SOME BASIC REPRESENTATION THEORY FOR COMPACT GROUPS 31
THE HAAR INTEGRAL 34
CONSEQUENCES OF HAAR MEASURE 35
THE MAIN THEOREM ON HILBERT MODULES FOR COMPACT GROUPS 37
POSTSCRIPT 49
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 50
CHAPTER 3. THE IDEAS OF PETER AND WEYL 51
PART 1: THE CLASSICAL THEOREM OF PETER AND WEYL 51
AN EXCURSION INTO LINEAR ALGEBRA 56
THE G-MODULES E' G E, HOM(-B, E) AND HOM(.E, E)' 58
THE FINE STRUCTURE OF R(G, K) 60
PART 2: THE GENERAL THEORY OF G-MODULES 67
VECTOR VALUED INTEGRATION 67
THE FIRST APPLICATION: THE AVERAGING OPERATOR 73
COMPACT GROUPS ACTING ON CONVEX CONES 77
MORE MODULE ACTIONS, CONVOLUTIONS 78
COMPLEXIFICATION OF REAL REPRESENTATIONS 83
POSTSCRIPT 89
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 89
CHAPTER 4. CHARACTERS 90
PART 1: CHARACTERS OF FINITE DIMENSIONAL REPRESENTATIONS 90
PART 2: THE STRUCTURE THEOREM OF E^ N 97
CYCLIC MODULES 108
POSTSCRIPT 109
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 110
HTTP://D-NB.INFO/1035031167
IMAGE 2
XVIII
CONTENTS
CHAPTER 5. LINEAR LIE GROUPS ILL
PRELIMINARIES ILL
THE EXPONENTIAL FUNCTION AND THE LOGARITHM 113
DIFFERENTIATING THE EXPONENTIAL FUNCTION IN A BANACH ALGEBRA 125
LOCAL GROUPS FOR THE CAMPBELL-HAUSDORFF MULTIPLICATION 131
SUBGROUPS OF A" 1 AND LINEAR LIE GROUPS 134
ANALYTIC GROUPS 138
THE INTRINSIC EXPONENTIAL FUNCTION OF A LINEAR LIE GROUP 139
THE ADJOINT REPRESENTATION OF A LINEAR LIE GROUP 146
SUBALGEBRAS, IDEALS, LIE SUBGROUPS, NORMAL LIE SUBGROUPS 151
NORMALIZERS, CENTRALIZERS, CENTERS 157
THE COMMUTATOR SUBGROUP 162
FORCED CONTINUITY OF MORPHISMS BETWEEN LIE GROUPS 166
QUOTIENTS OF LINEAR LIE GROUPS 169
THE TOPOLOGICAL SPLITTING THEOREM FOR NORMAL VECTOR SUBGROUPS 173
POSTSCRIPT 184
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 186
CHAPTER 6. COMPACT LIE GROUPS 187
COMPACT LIE ALGEBRAS 188
THE COMMUTATOR SUBGROUP OF A COMPACT LIE GROUP 199
THE STRUCTURE THEOREM FOR COMPACT LIE GROUPS 206
MAXIMAL TORI 210
THE SECOND STRUCTURE THEOREM FOR CONNECTED COMPACT LIE GROUPS 219
COMPACT ABELIAN LIE GROUPS AND THEIR LINEAR ACTIONS 224
ACTION OF A MAXIMAL TORUS ON THE LIE ALGEBRA 228
THE WEYL GROUP REVISITED 240
THE COMMUTATOR SUBGROUP OF CONNECTED COMPACT LIE GROUPS 251
ON THE AUTOMORPHISM GROUP OF A COMPACT LIE GROUP 252
COVERING GROUPS OF DISCONNECTED COMPACT LIE GROUPS 276
AUERBACH'S GENERATION THEOREM 278
THE TOPOLOGY OF CONNECTED COMPACT LIE GROUPS 286
POSTSCRIPT 296
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 298
CHAPTER 7. DUALITY OF ABELIAN TOPOLOGICAL GROUPS 299
THE COMPACT OPEN TOPOLOGY AND HOM-GROUPS 300
LOCAL COMPACTNESS AND DUALITY OF ABELIAN TOPOLOGICAL GROUPS 304 BASIC
FUNCTORIAL ASPECTS OF DUALITY 311
THE ANNIHILATOR MECHANISM 314
CHARACTER GROUPS OF TOPOLOGICAL VECTOR SPACES 325
THE EXPONENTIAL FUNCTION 340
WEIL'S LEMMA AND COMPACTLY GENERATED ABELIAN GROUPS 348
REDUCING LOCALLY COMPACT GROUPS TO COMPACT ABELIAN GROUPS 352 A MAJOR
STRUCTURE THEOREM 354
IMAGE 3
CONTENTS XIX
THE DUALITY THEOREM 357
THE IDENTITY COMPONENT 365
THE WEIGHT OF LOCALLY COMPACT ABELIAN GROUPS 368
POSTSCRIPT 370
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 373
CHAPTER 8. COMPACT ABELIAN GROUPS 374
PART 1: ASPECTS OF THE ALGEBRAIC STRUCTURE DIVISIBILITY, TORSION,
CONNECTIVITY 375
COMPACT ABELIAN GROUPS AS FACTOR GROUPS 381
PART 2: ASPECTS OF THE POINT SET TOPOLOGICAL STRUCTURE TOPOLOGICAL
DIMENSION OF COMPACT ABELIAN GROUPS 389
ARC CONNECTIVITY 396
LOCAL CONNECTIVITY 401
COMPACT METRIC ABELIAN GROUPS 413
PART 3: ASPECTS OF ALGEBRAIC TOPOLOGY-HOMOTOPY FREE COMPACT ABELIAN
GROUPS 417
HOMOTOPY OF COMPACT ABELIAN GROUPS 422
EXPONENTIAL FUNCTION AND HOMOTOPY 428
THE FINE STRUCTURE OF FREE COMPACT ABELIAN GROUPS 429
PART 4: ASPECTS OF HOMOLOGICAL ALGEBRA INJECTIVE, PROJECTIVE, AND FREE
COMPACT ABELIAN GROUPS 435
PART 5: ASPECTS OF ALGEBRAIC TOPOLOGY-COHOMOLOGY COHOMOLOGY OF COMPACT
ABELIAN GROUPS 440
PART 6: ASPECTS OF SET THEORY ARC COMPONENTS AND BOREL SUBSETS 445
POSTSCRIPT 449
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 451
CHAPTER 9. THE STRUCTURE OF COMPACT GROUPS 452
PART 1: THE FUNDAMENTAL STRUCTURE THEOREMS OF COMPACT GROUPS
APPROXIMATING COMPACT GROUPS BY COMPACT LIE GROUPS 453
THE CLOSEDNESS OF COMMUTATOR SUBGROUPS 454
SEMISIMPLE COMPACT CONNECTED GROUPS 455
THE LEVI-MAL'CEV STRUCTURE THEOREM FOR COMPACT GROUPS 469
MAXIMAL CONNECTED ABELIAN SUBGROUPS 477
THE SPLITTING STRUCTURE THEOREM 483
SUPPLEMENTING THE IDENTITY COMPONENT 484
PART 2: THE STRUCTURE THEOREMS FOR THE EXPONENTIAL FUNCTION THE
EXPONENTIAL FUNCTION OF COMPACT GROUPS 489
THE DIMENSION OF COMPACT GROUPS 496
LOCALLY EUCLIDEAN COMPACT GROUPS ARE COMPACT LIE GROUPS 502
PART 3: THE CONNECTIVITY STRUCTURE OF COMPACT GROUPS ARC CONNECTIVITY
506
LOCAL CONNECTIVITY 511
IMAGE 4
XX CONTENTS
COMPACT GROUPS AND INDECOMPOSABLE CONTINUA 514
PART 4: SOME HOMOLOGICAL ALGEBRA FOR COMPACT GROUPS THE PROJECTIVE COVER
OF CONNECTED COMPACT GROUPS 516
PART 5: THE AUTOMORPHISM GROUP OF COMPACT GROUPS 525
THE IWASAWA THEORY OF AUTOMORPHISM GROUPS 527
SIMPLE COMPACT GROUPS AND THE COUNTABLE LAYER THEOREM 535
THE STRUCTURE OF COMPACT FC-GROUPS 537
THE COMMUTATIVITY DEGREE OF A COMPACT GROUP 542
POSTSCRIPT 544
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 547
CHAPTER 10. COMPACT GROUP ACTIONS 548
A PREPARATION INVOLVING COMPACT SEMIGROUPS 549
ORBITS, ORBIT SPACE, AND ISOTROPY 549
EQUIVARIANCE AND CROSS SECTIONS 553
TRIVIALITY OF AN ACTION 558
QUOTIENT ACTIONS, TOTALLY DISCONNECTED G-SPACES 568
COMPACT LIE GROUP ACTIONS ON LOCALLY COMPACT SPACES 569
TRIVIALITY THEOREMS FOR COMPACT GROUP ACTIONS 571
SPLIT MORPHISMS 576
ACTIONS OF COMPACT GROUPS AND ACYCLICITY 589
FIXED POINTS OF COMPACT ABELIAN GROUP ACTIONS 591
TRANSITIVE ACTIONS OF COMPACT GROUPS 592
SZENTHE'S THEORY OF TRANSITIVE ACTIONS OF COMPACT GROUPS 594
POSTSCRIPT 605
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 608
CHAPTER 11. THE STRUCTURE OF FREE COMPACT GROUPS 609
THE CATEGORY THEORETICAL BACKGROUND 609
SPLITTING THE IDENTITY COMPONENT 614
THE CENTER OF A FREE COMPACT GROUP 615
THE COMMUTATOR SUBGROUP OF A FREE COMPACT GROUP 624
FREENESS VERSUS PROJECTIVITY 642
POSTSCRIPT 645
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 646
CHAPTER 12. CARDINAL INVARIANTS OF COMPACT GROUPS 647
SUITABLE SETS 647
GENERATING DEGREE AND DENSITY 652
THE CARDINAL INVARIANTS OF CONNECTED COMPACT GROUPS 656
CARDINAL INVARIANTS IN THE ABSENCE OF CONNECTIVITY 659
ON THE LOCATION OF SPECIAL GENERATING SETS 662
POSTSCRIPT 667
REFERENCES FOR THIS CHAPTER-ADDITIONAL READING 668
IMAGE 5
CONTENTS XXI
APPENDIX 1. ABELIAN GROUPS 669
EXAMPLES 669
FREE ABELIAN GROUPS 673
PROJECTIVE GROUPS 680
TORSION SUBGROUPS 681
PURE SUBGROUPS 682
FREE QUOTIENTS 684
DIVISIBILITY 685
SOME HOMOLOGICAL ALGEBRA 695
EXACT SEQUENCES 698
WHITEHEAD'S PROBLEM 709
POSTSCRIPT 722
REFERENCES FOR THIS APPENDIX-ADDITIONAL READING 722
APPENDIX 2. COVERING SPACES AND GROUPS 723
COVERING SPACES AND SIMPLE CONNECTIVITY 723
THE GROUP OF COVERING TRANSFORMATIONS 736
UNIVERSAL COVERING GROUPS 737
GROUPS GENERATED BY LOCAL GROUPS 739
POSTSCRIPT 743
REFERENCES FOR THIS APPENDIX-ADDITIONAL READING 744
APPENDIX 3. A PRIMER OF CATEGORY THEORY 745
CATEGORIES, MORPHISMS 745
POINTED CATEGORIES 753
TYPES OF MORPHISMS 754
FUNCTORS 762
NATURAL TRANSFORMATIONS 773
EQUIVALENCE OF CATEGORIES 777
LIMITS 778
THE CONTINUITY OF ADJOINTS 782
THE LEFT ADJOINT EXISTENCE THEOREM 782
COMMUTATIVE MONOIDAL CATEGORIES AND ITS MONOID OBJECTS 787
PART 1: THE QUINTESSENTIAL DIAGRAM CHASE 787
PART 2: CONNECTED GRADED COMMUTATIVE HOPF ALGEBRAS 797
PART 3: DUALITY OF GRADED HOPF ALGEBRAS 813
PART 4: AN APPLICATION TO COMPACT MONOIDS 815
POSTSCRIPT 817
REFERENCES FOR THIS APPENDIX-ADDITIONAL READING 818
APPENDIX 4. SELECTED RESULTS ON TOPOLOGY AND TOPOLOGICAL GROUPS 819 THE
ARC COMPONENT TOPOLOGY 819
THE WEIGHT OF A TOPOLOGICAL SPACE 822
METRIZABILITY OF TOPOLOGICAL GROUPS 827
DUALITY OF VECTOR SPACES 835
IMAGE 6
XXII CONTENTS
SUBGROUPS OF TOPOLOGICAL GROUPS 836
WALLACE'S LEMMA 838
CANTOR CUBES AND DYADIC SPACES 838
SOME BASIC FACTS ON COMPACT MONOIDS 840
POSTSCRIPT 843
REFERENCES FOR THIS APPENDIX-ADDITIONAL READING 844
APPENDIX 5. MEASURES ON COMPACT GROUPS 845
THE DEFINITION OF HAAR MEASURE 845
THE REQUIRED BACKGROUND OF RADON MEASURE THEORY 845
PRODUCT MEASURES 846
THE SUPPORT OF A MEASURE 847
MEASURES ON COMPACT GROUPS: CONVOLUTION 849
SEMIGROUP THEORETICAL CHARACTERIZATION OF HAAR MEASURE 852
IDEMPOTENT PROBABILITY MEASURES ON A COMPACT GROUP 853
ACTIONS AND PRODUCT MEASURES 854
POSTSCRIPT 860
REFERENCES FOR THIS APPENDIX-ADDITIONAL READING 860
APPENDIX 6. PROJECTIVE LIMITS OF WELL-ORDERED INVERSE SYSTEMS . . 861
WELL-ORDERED LIE CHAINS 861
SUPERCOMPACTNESS 864
COMPACT HOMEOMORPHISM GROUPS 865
POSTSCRIPT 866
REFERENCES FOR THIS APPENDIX-ADDITIONAL READING 866
REFERENCES 867
INDEX OF SYMBOLS 884
INDEX 886 |
| any_adam_object | 1 |
| author | Hofmann, Karl H. 1932- Morris, Sidney A. 1947- |
| author_GND | (DE-588)115780734 (DE-588)132019515 |
| author_facet | Hofmann, Karl H. 1932- Morris, Sidney A. 1947- |
| author_role | aut aut |
| author_sort | Hofmann, Karl H. 1932- |
| author_variant | k h h kh khh s a m sa sam |
| building | Verbundindex |
| bvnumber | BV041249312 |
| classification_rvk | SK 260 SK 340 |
| ctrlnum | (OCoLC)858923888 (DE-599)DNB1035031167 |
| dewey-full | 510 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510 |
| dewey-search | 510 |
| dewey-sort | 3510 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| edition | 3. ed., revised and augmented |
| format | Book |
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| id | DE-604.BV041249312 |
| illustrated | Illustrated |
| indexdate | 2024-08-03T00:54:05Z |
| institution | BVB |
| isbn | 3110296551 9783110296556 9783110296808 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-026223382 |
| oclc_num | 858923888 |
| open_access_boolean | |
| owner | DE-20 DE-19 DE-BY-UBM DE-29T DE-703 |
| owner_facet | DE-20 DE-19 DE-BY-UBM DE-29T DE-703 |
| physical | XXII, 924 S. graph. Darst. 240 mm x 170 mm |
| publishDate | 2013 |
| publishDateSearch | 2013 |
| publishDateSort | 2013 |
| publisher | De Gruyter |
| record_format | marc |
| series | De Gruyter Studies in Mathematics |
| series2 | De Gruyter Studies in Mathematics |
| spelling | Hofmann, Karl H. 1932- Verfasser (DE-588)115780734 aut The structure of compact groups a primer for the student ; a handbook for the expert Karl H. Hofmann ; Sidney A. Morris 3. ed., revised and augmented Berlin [u.a.] De Gruyter 2013 XXII, 924 S. graph. Darst. 240 mm x 170 mm txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematics 25 Literaturverz. S. [867] - 884 Kompakte Gruppe (DE-588)4164840-7 gnd rswk-swf Kompakte Gruppe (DE-588)4164840-7 s DE-604 Morris, Sidney A. 1947- Verfasser (DE-588)132019515 aut Erscheint auch als Online-Ausgabe 978-3-11-029679-2 De Gruyter Studies in Mathematics 25 (DE-604)BV000005407 25 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4347480&prov=M&dok_var=1&dok_ext=htm Inhaltstext DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026223382&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hofmann, Karl H. 1932- Morris, Sidney A. 1947- The structure of compact groups a primer for the student ; a handbook for the expert De Gruyter Studies in Mathematics Kompakte Gruppe (DE-588)4164840-7 gnd |
| subject_GND | (DE-588)4164840-7 |
| title | The structure of compact groups a primer for the student ; a handbook for the expert |
| title_auth | The structure of compact groups a primer for the student ; a handbook for the expert |
| title_exact_search | The structure of compact groups a primer for the student ; a handbook for the expert |
| title_full | The structure of compact groups a primer for the student ; a handbook for the expert Karl H. Hofmann ; Sidney A. Morris |
| title_fullStr | The structure of compact groups a primer for the student ; a handbook for the expert Karl H. Hofmann ; Sidney A. Morris |
| title_full_unstemmed | The structure of compact groups a primer for the student ; a handbook for the expert Karl H. Hofmann ; Sidney A. Morris |
| title_short | The structure of compact groups |
| title_sort | the structure of compact groups a primer for the student a handbook for the expert |
| title_sub | a primer for the student ; a handbook for the expert |
| topic | Kompakte Gruppe (DE-588)4164840-7 gnd |
| topic_facet | Kompakte Gruppe |
| url | http://deposit.dnb.de/cgi-bin/dokserv?id=4347480&prov=M&dok_var=1&dok_ext=htm http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026223382&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000005407 |
| work_keys_str_mv | AT hofmannkarlh thestructureofcompactgroupsaprimerforthestudentahandbookfortheexpert AT morrissidneya thestructureofcompactgroupsaprimerforthestudentahandbookfortheexpert |