The structure of compact groups : a primer for students, a handbook for the expert

The structure of compact groups : a primer for students, a handbook for the expert /

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Bibliographic Details
Main Author: Hofmann, Karl Heinrich
Corporate Author: Ebooks Corporation
Other Authors: Morris, Sidney A., 1947-
Format: Electronic eBook
Language:English
Published: Berlin ; Boston : Walter de Gruyter GmbH & Co., KG, [2013]
Edition:Third edition, revised and augmented
Series:De Gruyter studies in mathematics ; 25.
Subjects:
Compact groups.
Online Access:Connect to this title online (unlimited simultaneous users allowed; 325 uses per year)

MARC

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100 1 |a Hofmann, Karl Heinrich. 
245 1 4 |a The structure of compact groups :  |b a primer for students, a handbook for the expert /  |c Karl H. Hofmann, Sidney A. Morris. 
250 |a Third edition, revised and augmented 
260 |a Berlin ;  |a Boston :  |b Walter de Gruyter GmbH & Co., KG,  |c [2013] 
300 |a 1 online resource (xxii, 924 pages) :  |b illustrations. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
490 1 |a De Gruyter studies in mathematics ;  |v 25 
533 |a Electronic reproduction.  |b Perth, W.A.  |n Available via World Wide Web. 
588 |a Description based on print version record. 
505 0 0 |a Machine generated contents note:   |g ch. 1   |t Basic Topics and Examples --   |t Definitions and Elementary Examples --   |t Actions, Subgroups, Quotient Spaces --   |t Products of Compact Groups --   |t Applications to Abelian Groups --   |t Projective Limits --   |t Totally Disconnected Compact Groups --   |t Some Duality Theory --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g ch. 2   |t Basic Representation Theory of Compact Groups --   |t Some Basic Representation Theory for Compact Groups --   |t Haar Integral --   |t Consequences of Haar Measure --   |t Main Theorem on Hilbert Modules for Compact Groups --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g ch. 3   |t Ideas of Peter and Weyl --   |g pt. 1   |t Classical Theorem of Peter and Weyl --   |t Excursion into Linear Algebra --   |t G-modules E' [⊗] E, Hom(E, E) and Hom(E, E)' --   |t Fine Structure of R(G, K) --   |g pt. 2   |t General Theory of G-Modules --   |t Vector Valued Integration --   |t First Application: The Averaging Operator --   |t Compact Groups Acting on Convex Cones --   |t More Module Actions, Convolutions --   |t Complexification of Real Representations --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g ch. 4   |t Characters --   |g pt. 1   |t Characters of Finite Dimensional Representations --   |g pt. 2   |t Structure Theorem of Efin --   |t Cyclic Modules --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g ch. 5   |t Linear Lie Groups --   |t Preliminaries --   |t Exponential Function and the Logarithm --   |t Differentiating the Exponential Function in a Banach Algebra --   |t Local Groups for the Campbell--Hausdorff Multiplication --   |t Subgroups of A--1 and Linear Lie Groups --   |t Analytic Groups --   |t Intrinsic Exponential Function of a Linear Lie Group --   |t Adjoint Representation of a Linear Lie Group --   |t Subalgebras, Ideals, Lie Subgroups, Normal Lie Subgroups --   |t Normalizers, Centralizers, Centers --   |t Commutator Subgroup --   |t Forced Continuity of Morphisms between Lie Groups --   |t Quotients of Linear Lie Groups --   |t Topological Splitting Theorem for Normal Vector Subgroups --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g ch. 6   |t Compact Lie Groups --   |t Compact Lie algebras --   |t Commutator Subgroup of a Compact Lie Group --   |t Structure Theorem for Compact Lie Groups --   |t Maximal Tori --   |t Second Structure Theorem for Connected Compact Lie Groups --   |t Compact Abelian Lie Groups and their Linear Actions --   |t Action of a Maximal Torus on the Lie Algebra --   |t Weyl Group Revisited --   |t Commutator Subgroup of Connected Compact Lie Groups --   |t On the Automorphism Group of a Compact Lie Group --   |t Covering Groups of Disconnected Compact Lie Groups --   |t Auerbach's Generation Theorem --   |t Topology of Connected Compact Lie Groups --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g ch. 7   |t Duality of Abelian Topological Groups --   |t Compact Open Topology and Hom-Groups --   |t Local Compactness and Duality of Abelian Topological Groups --   |t Basic Functorial Aspects of Duality --   |t Annihilator Mechanism --   |t Character Groups of Topological Vector Spaces --   |t Exponential Function --   |t Weil's Lemma and Compactly Generated Abelian Groups --   |t Reducing Locally Compact Groups to Compact Abelian Groups --   |t Major Structure Theorem --   |t Duality Theorem --   |t Identity Component --   |t Weight of Locally Compact Abelian Groups --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g ch. 8   |t Compact Abelian Groups --   |g pt. 1   |t Aspects of the Algebraic Structure Divisibility, Torsion, Connectivity --   |t Compact Abelian Groups as Factor Groups --   |g pt. 2   |t Aspects of the Point Set Topological Structure Topological Dimension of Compact Abelian Groups --   |t Arc Connectivity --   |t Local Connectivity --   |t Compact Metric Abelian Groups --   |g pt. 3   |t Aspects of Algebraic Topology---Homotopy Free Compact Abelian Groups --   |t Homotopy of Compact Abelian Groups --   |t Exponential Function and Homotopy --   |t Fine Structure of Free Compact Abelian Groups --   |g pt. 4   |t Aspects of Homological Algebra Injective, Projective, and Free Compact Abelian Groups --   |g pt. 5   |t Aspects of Algebraic Topology---Cohomology Cohomology of Compact Abelian Groups --   |g pt. 6   |t Aspects of Set Theory Arc Components and Borel Subsets --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g ch. 9   |t Structure of Compact Groups --   |g pt. 1   |t Fundamental Structure Theorems of Compact Groups Approximating Compact Groups by Compact Lie Groups --   |t Closedness of Commutator Subgroups --   |t Semisimple Compact Connected Groups --   |t Levi--Mal'cev Structure Theorem for Compact Groups --   |t Maximal Connected Abelian Subgroups --   |t Splitting Structure Theorem --   |t Supplementing the Identity Component --   |g pt. 2   |t Structure Theorems for the Exponential Function The Exponential Function of Compact Groups --   |t Dimension of Compact Groups --   |t Locally Euclidean Compact Groups Are Compact Lie Groups --   |g pt. 3   |t Connectivity Structure of Compact Groups Arc Connectivity --   |t Local Connectivity --   |t Compact Groups and Indecomposable Continua --   |g pt. 4   |t Some Homological Algebra for Compact Groups The Projective Cover of Connected Compact Groups --   |g pt. 5   |t Automorphism Group of Compact Groups --   |t Iwasawa Theory of Automorphism Groups --   |t Simple Compact Groups and the Countable Layer Theorem --   |t Structure of Compact FC-Groups --   |t Commutativity Degree of a Compact Group --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g ch. 10   |t Compact Group Actions --   |t Preparation Involving Compact Semigroups --   |t Orbits, Orbit Space, and Isotropy --   |t Equivariance and Cross Sections --   |t Triviality of an Action --   |t Quotient Actions, Totally Disconnected G-Spaces --   |t Compact Lie Group Actions on Locally Compact Spaces --   |t Triviality Theorems for Compact Group Actions --   |t Split Morphisms --   |t Actions of Compact Groups and Acyclicity --   |t Fixed Points of Compact Abelian Group Actions --   |t Transitive Actions of Compact Groups --   |t Szenthe's Theory of Transitive Actions of Compact Groups --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g ch. 11   |t Structure of Free Compact Groups --   |t Category Theoretical Background --   |t Splitting the Identity Component --   |t Center of a Free Compact Group --   |t Commutator Subgroup of a Free Compact Group --   |t Freeness Versus Projectivity --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g ch. 12   |t Cardinal Invariants of Compact Groups --   |t Suitable Sets --   |t Generating Degree and Density --   |t Cardinal Invariants of Connected Compact Groups --   |t Cardinal Invariants in the Absence of Connectivity --   |t On the Location of Special Generating Sets --   |t Postscript --   |t References for this Chapter---Additional Reading --   |g Appendix 1   |t Abelian Groups --   |t Examples --   |t Free Abelian Groups --   |t Projective Groups --   |t Torsion Subgroups --   |t Pure Subgroups --   |t Free Quotients --   |t Divisibility --   |t Some Homological Algebra --   |t Exact Sequences --   |t Whitehead's Problem --   |t Postscript --   |t References for this Appendix---Additional Reading --   |g Appendix 2   |t Covering Spaces and Groups --   |t Covering Spaces and Simple Connectivity --   |t Group of Covering Transformations --   |t Universal Covering Groups --   |t Groups Generated by Local Groups --   |t Postscript --   |t References for this Appendix---Additional Reading --   |g Appendix 3   |t Primer of Category Theory --   |t Categories, Morphisms --   |t Pointed Categories --   |t Types of Morphisms --   |t Functors --   |t Natural Transformations --   |t Equivalence of Categories --   |t Limits --   |t Continuity of Adjoints --   |t Left Adjoint Existence Theorem --   |t Commutative Monoidal Categories and its Monoid Objects --   |g pt. 1   |t Quintessential Diagram Chase --   |g pt. 2   |t Connected Graded Commutative Hopf Algebras --   |g pt. 3   |t Duality of Graded Hopf Algebras --   |g pt. 4   |t Application to Compact Monoids --   |t Postscript --   |t References for this Appendix---Additional Reading --   |g Appendix 4   |t Selected Results on Topology and Topological Groups --   |t Arc Component Topology --   |t Weight of a Topological Space --   |t Metrizability of Topological Groups --   |t Duality of Vector Spaces --   |t Subgroups of Topological Groups --   |t Wallace's Lemma --   |t Cantor Cubes and Dyadic Spaces --   |t Some Basic Facts on Compact Monoids --   |t Postscript --   |t References for this Appendix---Additional Reading --   |g Appendix 5   |t Measures on Compact Groups --   |t Definition of Haar Measure --   |t Required Background of Radon Measure Theory --   |t Product Measures --   |t Support of a Measure --   |t Measures on Compact Groups: Convolution --   |t Semigroup Theoretical Characterization of Haar Measure --   |t Idempotent Probability Measures on a Compact Group --   |t Actions and Product Measures --   |t Postscript --   |t References for this Appendix---Additional Reading --   |g Appendix 6   |t Projective Limits of Well-Ordered Inverse Systems --   |t Well-ordered Lie chains --   |t Supercompactness --   |t Compact Homeomorphism Groups --   |t Postscript --   |t References for this Appendix---Additional Reading. 
504 |a Includes bibliographical references (pages [867]-884) and indexes. 
650 0 |a Compact groups. 
700 1 |a Morris, Sidney A.,  |d 1947- 
710 2 |a Ebooks Corporation 
776 0 8 |c Original  |z 9783110296556  |z 3110296551  |w (DLC) 2013020147 
830 0 |a De Gruyter studies in mathematics ;  |v 25. 
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