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The Structure of Compact Groups
A Primer for the Student – A Handbook for the Expert
-
Karl H. Hofmann
Language:
English
Published/Copyright:
2020
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 / Editor information
Karl H. Hofmann, TU Darmstadt, Germany, Tulane University, USA; Sidney A. Morris, University of Ballarat, LaTrobe University, Australia
Topics
-
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Frontmatter
i -
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Preface to the Fourth Edition
vii -
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Preface to the Second and Third Editions
x -
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Preface to the First Edition
xiv -
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The Logical Dependence of the Contents
xix -
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Contents
xxi -
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Chapter 1. Basic Topics and Examples
1 -
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Chapter 2. The Basic Representation Theory of Compact Groups
31 -
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Chapter 3. The Ideas of Peter and Weyl
51 -
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Chapter 4. Characters
126 -
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Chapter 5. Linear Lie Groups
147 -
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Chapter 6. Compact Lie Groups
223 -
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Chapter 7. Duality of Abelian Topological Groups
336 -
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Chapter 8. Compact Abelian Groups
407 -
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Chapter 9. The Structure of Compact Groups
486 -
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Chapter 10. Compact Group Actions
582 -
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Chapter 11. The Structure of Free Compact Groups
644 -
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Chapter 12. Cardinal Invariants of Compact Groups
682 -
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Appendix 1. Abelian Groups
706 -
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Appendix 2. Covering Spaces and Groups
761 -
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Appendix 3. A Primer of Category Theory
783 -
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Appendix 4. Selected Results on Topology and Topological Groups
864 -
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Appendix 5. Measures on Compact Groups
890 -
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Appendix 6. Well-Ordered Projective Limits, Supercompactness, and Compact Homeomorphism Groups
909 -
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Appendix 7. Weakly Complete Vector Spaces and Algebras
915 -
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References
945 -
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Index of Symbols
965 -
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Index
968
Publishing information
Pages and Images/Illustrations in book
eBook published on:
June 8, 2020
eBook ISBN:
9783110695991
Edition:
4th revised and expanded edition
Pages and Images/Illustrations in book
Front matter:
28
Main content:
1006
Illustrations:
3
Tables:
2
eBook ISBN:
9783110695991
Keywords for this book
compact groups; Topological groups; Lie algebra; Category Theory; Abelian Groups
Audience(s) for this book
Graduate students with sufficient knowledge in analysis, algebra, and topology; experts in group theory.
