The Structure of Compact Groups

Karl H. Hofmann; Sidney A. Morris

Published by De Gruyter 2020

The Structure of Compact Groups

A Primer for the Student – A Handbook for the Expert

Karl H. Hofmann

and Sidney A. Morris

Volume 25 in the series De Gruyter Studies in Mathematics

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

Topics

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

(Deutsch)

Language: English
Publisher: De Gruyter
Edition: 4th revised and expanded edition
Audience: Graduate students with sufficient knowledge in analysis, algebra, and topology; experts in group theory.
Pages
- Front matter: 28
- Main content: 1006
Illustrations
- Illustrations: 3
- Tables: 2
Keywords: compact groups; Topological groups; Lie algebra; Category Theory; Abelian Groups

eBook

Published: June 8, 2020
ISBN: 9783110695991

Hardcover

Published: June 8, 2020
ISBN: 9783110695953