Holdings: The structure of compact groups

The structure of compact groups: a primer for the student ; a handbook for the expert

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Bibliographic Details
Main Authors:	Hofmann, Karl H. 1932- (Author), Morris, Sidney A. 1947- (Author)
Format:	Book
Language:	English
Published:	Berlin [u.a.] De Gruyter 2013
Edition:	3. ed., revised and augmented
Series:	De Gruyter Studies in Mathematics 25
Subjects:	Kompakte Gruppe
Online Access:	Inhaltstext Inhaltsverzeichnis
Item Description:	Literaturverz. S. [867] - 884
Physical Description:	XXII, 924 S. graph. Darst. 240 mm x 170 mm
ISBN:	3110296551 9783110296556 9783110296808

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MARC


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Record in the Search Index

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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
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author	Hofmann, Karl H. 1932- Morris, Sidney A. 1947-
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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
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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
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