The Structure of Compact Groups: A Primer for the Student - A Handbook for the Expert

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Walter de Gruyter, Aug 29, 2013 - Mathematics - 946 pages
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The subject matter of compact groups is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics. This book serves the dual purpose of providing a textbook on it for upper level graduate courses or seminars, and of serving as a source book for research specialists who need to apply the structure and representation theory of compact groups.

After a gentle introduction to compact groups and their representation theory, the book presents self-contained courses on linear Lie groups, on compact Lie groups, and on locally compact abelian groups. Separate appended chapters contain the material for courses on abelian groups and on category theory. However, the thrust of the book points in the direction of the structure theory of not necessarily finite dimensional, nor necessarily commutative, compact groups, unfettered by weight restrictions or dimensional bounds. In the process it utilizes infinite dimensional Lie algebras and the exponential function of arbitrary compact groups.

The first edition of 1998 and the second edition of 2006 were well received by reviewers and have been frequently quoted in the areas of instruction and research. For the present new edition the text has been cleaned of typographical flaws and the content has been conceptually sharpened in some places and polished and improved in others. New material has been added to various sections taking into account the progress of research on compact groups both by the authors and other writers. Motivation was provided, among other things, by questions about the structure of compact groups put to the authors by readers through the years following the earlier editions. Accordingly, the authors wished to clarify some aspects of the book which they felt needed improvement. The list of references has increased as the authors included recent publications pertinent to the content of the book.

 

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Contents

Chapter 1 Basic Topics and Examples
1
Chapter 2 The Basic Representation Theory of Compact Groups
31
Chapter 3 The Ideas of Peter and Weyl
51
Chapter 4 Characters
90
Chapter 5 Linear Lie Groups
111
Chapter 6 Compact Lie Groups
187
Chapter 7 Duality of Abelian Topological Groups
299
Chapter 8 Compact Abelian Groups
374
Chapter 12 Cardinal Invariants of Compact Groups
647
Appendix 1 Abelian Groups
669
Appendix 2 Covering Spaces and Groups
723
Appendix 3 A Primer of Category Theory
745
Appendix 4 Selected Results on Topology and Topological Groups
819
Appendix 5 Measures on Compact Groups
845
Appendix 6 Projective Limits of WellOrdered Inverse Systems
861
References
867

Chapter 9 The Structure of Compact Groups
452
Chapter 10 Compact Group Actions
548
Chapter 11 The Structure of Free Compact Groups
609
Index of Symbols
884
Index
886
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About the author (2013)

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

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