The structure of compact groups: a primer for the student - a handbook for the expert
Gespeichert in:
| Beteiligte Personen: | , |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
Berlin ; New York
<<de>> Gruyter
2006
|
| Ausgabe: | 2., rev. and augm. ed. |
| Schriftenreihe: | De Gruyter studies in mathematics
25 |
| Schlagwörter: | |
| Links: | http://deposit.dnb.de/cgi-bin/dokserv?id=2800662&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=015476245&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Beschreibung: | Literaturverz. S. 805 - 819 |
| Umfang: | XVII, 858 S. graph. Darst. 25 cm |
| ISBN: | 9783110190069 3110190060 |
Internformat
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| 264 | 1 | |a Berlin ; New York |b <<de>> Gruyter |c 2006 | |
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Datensatz im Suchindex
| _version_ | 1819337679455649792 |
|---|---|
| adam_text | Contents
Chapter
Definitions and Elementary Examples
Actions, Subgroups, Quotient Spaces
Products of Compact Groups
Applications to Abelian Groups
Projective
Totally Disconnected Compact Groups
Some Duality Theory
Postscript
References for this Chapter
Chapter
Some Basic Representation Theory for Compact Groups
The
Consequences of
The Main Theorem on Hubert Modules for Compact Groups
Postscript
References for this Chapter
Chapter
Part
An Excursion into Linear Algebra
The G-modules E <g> E, Hom^, E) and Hom^, E)
The Fine Structure of R(G, K)
Part
Vector Valued Integration
The First Application: The Averaging Operator
Compact Groups Acting on Convex Cones
More Module Actions, Convolutions
Complexification of Real Representations
Postscript
References for this Chapter
Chapter
Part
Part
Cyclic Modules
Postscript
References for this Chapter
xiv Contents
Chapter
Preliminaries
The Exponential Function and the Logarithm
Differentiating the Exponential Function in a Banach Algebra
Local Groups for the Campbell-Hausdorff Multiplication
Subgroups of
Analytic Groups
The Intrinsic Exponential Function of a Linear Lie Group
The Adjoint Representation of a Linear Lie Group
Subalgebras, Ideals, Lie Subgroups, Normal Lie Subgroups
Normalizers, Centralizers, Centers
The Commutator Subgroup
Forced Continuity of Morphisms between Lie Groups
Quotients of Linear Lie Groups
The Topological Splitting Theorem for Normal Vector Subgroups
Postscript
References for this Chapter
Chapter
Compact Lie algebras
The Commutator Subgroup of a Compact Lie Group
The Structure Theorem for Compact Lie Groups
Maximal Tori
Lee s Theorem: Preliminary Version
The Second Structure Theorem for Connected Compact Lie Groups
Compact Abelian Lie Groups and Their Linear Actions
Action of a Maximal Torus on the Lie Algebra
The Weyl Group Revisited
The Commutator Subgroup of Connected Compact Lie Groups
On the Automorphism Group of a Compact Lie Group
Covering Groups of Disconnected Compact Lie Groups
Auerbach s Generation Theorem
The Topology of Connected Compact Lie Groups
Postscript
References for this Chapter
Chapter
The Compact Open Topology and Hom-Groups
Local Compactness and Duality of Abelian Topological Groups
Basic Functorial Aspects of Duality
The Annihilator Mechanism
Character Groups of Topological Vector Spaces
The Exponential Function
Weil s Lemma and Compactly Generated Abelian Groups
Reducing Locally Compact Groups to Compact Abelian Groups
Contents xv
The Duality Theorem
The Identity Component
The Weight of Locally Compact Abelian Groups
Postscript
References for this Chapter
Chapter
Part
Divisibility, Torsion, Connectivity
Compact Abelian Groups as Factor Groups
Part
Topological Dimension of Compact Abelian Groups
Arc Connectivity
Local Connectivity
Compact Metric Abelian Groups
Part
Free Compact Abelian Groups
Homotopy of Compact Abelian Groups
Exponential Function and Homotopy
The Fine Structure of Free Compact Abelian Groups
Part
Injective,
Part
Cohomology of Compact Abelian Groups
Part
Arc Components and
Postscript
References for this Chapter
Chapter
Part
Approximating Compact Groups by Compact Lie Groups
The Closedness of Commutator Subgroups
Semisimple
The Levi-Mal cev Structure Theorem for Compact Groups
Maximal Connected Abelian Subgroups
The Splitting Structure Theorem
Supplementing the Identity Component
Part
The Exponential Function of Compact Groups
The Dimension of Compact Groups
Locally Euclidean Compact Groups Are Compact Lie Groups
Part
Arc Connectivity
Local Connectivity
xvi Contents
Compact
Part
The
Part
The Iwasawa Theory of Automorphism Groups
Simple Compact Groups and the Countable Layer Theorem
Postscript
References for this Chapter
Chapter
A Preparation Involving Compact Semigroups
Orbits, Orbit Space, and Isotropy
Equivariance and Cross Sections
The Triviality Theorem
Quotient Actions, Totally Disconnected G-Spaces
Compact Lie Group Actions on Locally Compact Spaces
Triviality Theorem for Compact Group Actions
Split Morphisms
Postscript
References for this Chapter
Chapter
The Category Theoretical Background
Splitting the Identity Component
The Center of a Free Compact Group
The Commutator Subgroup of a Free Compact Group
Freeness Versus Projectivity
Postscript
References for this Chapter
Chapter
Suitable Sets
Generating Degree and Density
The Cardinal Invariants of Connected Compact Groups
Cardinal Invariants in the Absence of Connectivity
On the Location of Special Generating Sets
Postscript
References for this Chapter
Appendix
Examples
Free
Projective
Torsion Subgroups
Pure Subgroups
Contents xvii
Free Quotients
Divisibility
Some Homological Algebra
Exact Sequences
Whitehead s Problem
Postscript
References for this Chapter
Appendix
Covering Spaces and Simple Connectivity
The Group of Covering Transformations
Universal Covering Groups
Groups Generated by Local Groups
Postscript
References for this Chapter
Appendix
Categories, Morphisms
Pointed Categories
Types of Morphisms
Functors
Natural Transformations
Equivalence of Categories
Limits
Continuity of
The Left Adjoint Existence Theorem
Commutative Monoidal Categories and its Monoid Objects
Part
Part
Part
Part
Postscript
References for this Chapter
Appendix
The Arc Component Topology
The Weight of a Topological Space
Metrizability of Topological Groups
Duality of Vector Spaces
Subgroups of Topological Groups
Postscript
References for this Chapter
References
List of Symbols
Index
|
| any_adam_object | 1 |
| author | Hofmann, Karl H. 1932- Morris, Sidney A. 1947- |
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| 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 | BV022265665 |
| classification_rvk | SK 340 |
| ctrlnum | (OCoLC)180912322 (DE-599)BVBBV022265665 |
| discipline | Mathematik |
| edition | 2., rev. and augm. ed. |
| format | Book |
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| id | DE-604.BV022265665 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T12:51:26Z |
| institution | BVB |
| isbn | 9783110190069 3110190060 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-015476245 |
| oclc_num | 180912322 |
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| owner_facet | DE-824 DE-355 DE-BY-UBR DE-11 |
| physical | XVII, 858 S. graph. Darst. 25 cm |
| publishDate | 2006 |
| publishDateSearch | 2006 |
| publishDateSort | 2006 |
| publisher | <<de>> Gruyter |
| record_format | marc |
| series | De Gruyter studies in mathematics |
| series2 | De Gruyter studies in mathematics |
| 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 |
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