The Structure of Compact Groups

Karl H. Hofmann; Sidney A. Morris

Karl H. Hofmann and Sidney A. Morris

The Structure of Compact Groups

A Primer for the Student – A Handbook for the Expert

In: De Gruyter Studies in Mathematics, 25

De Gruyter | 2020

https://doi.org/10.1515/9783110695991

Overview
Contents

About this book

This book is designed both as a textbook for high-level graduate courses and as a reference for researchers who need to apply the structure and representation theory of compact groups. A gentle introduction to compact groups and their representation theory is followed by self-contained courses on linear and compact Lie groups, and on locally compact abelian groups.

This fourth edition was updated with the latest developments in the field.

Thorough introduction to compact groups, which have applications in algebra, topology, functional analysis, and theoretical physics.
Thrust of the book points to structure theory of infinite dimensional, not necessarily commutative compact groups.

Author information

Karl H. Hofmann, TU Darmstadt, Germany, Tulane University, USA; Sidney A. Morris, University of Ballarat, LaTrobe University, Australia

Frontmatter Accessible PDF	i
Preface to the Fourth Edition Accessible PDF	vii
Preface to the Second and Third Editions Accessible PDF	x
Preface to the First Edition Accessible PDF	xiv
The Logical Dependence of the Contents Accessible PDF	xix
Contents Accessible PDF	xxi
Chapter 1. Basic Topics and Examples Requires Authentication Accessible PDF	1
Chapter 2. The Basic Representation Theory of Compact Groups Requires Authentication Accessible PDF	31
Chapter 3. The Ideas of Peter and Weyl Requires Authentication Accessible PDF	51
Chapter 4. Characters Requires Authentication Accessible PDF	126
Chapter 5. Linear Lie Groups Requires Authentication Accessible PDF	147
Chapter 6. Compact Lie Groups Requires Authentication Accessible PDF	223
Chapter 7. Duality of Abelian Topological Groups Requires Authentication Accessible PDF	336
Chapter 8. Compact Abelian Groups Requires Authentication Accessible PDF	407
Chapter 9. The Structure of Compact Groups Requires Authentication Accessible PDF	486
Chapter 10. Compact Group Actions Requires Authentication Accessible PDF	582
Chapter 11. The Structure of Free Compact Groups Requires Authentication Accessible PDF	644
Chapter 12. Cardinal Invariants of Compact Groups Requires Authentication Accessible PDF	682
Appendix 1. Abelian Groups Requires Authentication Accessible PDF	706
Appendix 2. Covering Spaces and Groups Requires Authentication Accessible PDF	761
Appendix 3. A Primer of Category Theory Requires Authentication Accessible PDF	783
Appendix 4. Selected Results on Topology and Topological Groups Requires Authentication Accessible PDF	864
Appendix 5. Measures on Compact Groups Requires Authentication Accessible PDF	890
Appendix 6. Well-Ordered Projective Limits, Supercompactness, and Compact Homeomorphism Groups Requires Authentication Accessible PDF	909
Appendix 7. Weakly Complete Vector Spaces and Algebras Requires Authentication Accessible PDF	915
References Requires Authentication Accessible PDF	945
Index of Symbols Requires Authentication Accessible PDF	965
Index Requires Authentication Accessible PDF	968

(Deutsch)

The Structure of Compact Groups

A Primer for the Student – A Handbook for the Expert

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