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 ; New York <<de>> Gruyter 2006
Edition:	2., rev. and augm. ed.
Series:	De Gruyter studies in mathematics 25
Subjects:	Kompakte Gruppe
Online Access:	Inhaltstext Inhaltsverzeichnis
Item Description:	Literaturverz. S. 805 - 819
Physical Description:	XVII, 858 S. graph. Darst. 25 cm
ISBN:	9783110190069 3110190060

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MARC


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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
adam_txt	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
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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 2., rev. and augm. ed. Berlin ; New York <<de>> Gruyter 2006 XVII, 858 S. graph. Darst. 25 cm txt rdacontent n rdamedia nc rdacarrier De Gruyter studies in mathematics 25 Literaturverz. S. 805 - 819 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 De Gruyter studies in mathematics 25 (DE-604)BV004069300 25 text/html http://deposit.dnb.de/cgi-bin/dokserv?id=2800662&prov=M&dok_var=1&dok_ext=htm Inhaltstext Digitalisierung UB Regensburg application/pdf 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 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_exact_search_txtP	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
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