The Structure of Compact Groups

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.

„Altogether, this book is a must for everybody who is interested in topological groups." Internationale Mathematische Nachrichten

"Each chapter and appendix has a short preface of introductory nature and a historical and theoretical postscript and is completed with a list of corresponding references. Many examples are discussed, which are mainly of general interest, and the book is endowed with many exercises, almost all of which are of the form "prove the previous assertion'' (which stresses the role of the book as both a "primer for the student'' and a "handbook for the expert''). Thus, the book is very informative. The text is quite understandable and well written (as are other texts by the authors). [...] The book by Hofmann and Morris is fresh and promising, and its ideas, approaches, and results advance the structure theory of more general topological groups; thus, it is guaranteed a vast audience." Mathematical Reviews (review of the first edition)