The Structure of Compact Groups: A Primer for Students - a Handbook for the Expert (De Gruyter Studies in Mathematics)

Dealing with subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book has been conceived with the dual purpose of providing a text book 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. However, the thrust of book points in the direction of the structure theory of infinite dimensional, not 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 was well received by reviewers and has been frequently quoted in the areas of instruction and research. For the present new edition the text has been cleaned of typographical flaws and some minor inaccuracies of content; it has been edited and improved in various sections. New material has been added in order to reflect ongoing research. In the process of revising the original edition, the integrity of the original section numbering was carefully respected so that citations of material from the first edition remains perfectly viable to the users of this edition. Dealing with the subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics, this book has been conceived with the dual purpose of providing a text book 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. The first edition of 1998 was well received by reviewers and has been frequently quoted in the areas of instruction and research. For the present new edition the text has been improved in various sections. New material has been added in order to reflect ongoing research. Frontmatter Contents Chapter 1 Basic Topics and Examples Chapter 2 The Basic Representation Theory of Compact Groups Chapter 3 The Ideas of Peter and Weyl Chapter 4 Characters Chapter 5 Linear Lie Groups Chapter 6 Compact Lie Groups Chapter 7 Duality for Abelian Topological Groups Chapter 8 Compact Abelian Groups Chapter 9 The Structure of Compact Groups Chapter 10 Compact Group Actions Chapter 11 The Structure of Free Compact Groups Chapter 12 Cardinal Invariants of Compact Groups Backmatter Deals with the subject matter of compact groups that is frequently cited in fields like algebra, topology, functional analysis, and theoretical physics. This book is suitable for upper level graduate courses or seminars. It is useful for research specialists who need to apply the structure and representation theory of compact groups Review text: "Thus, the book is informative and carefully written; the exposition is fresh and excellent. It can be useful for students as well as for experts and will meet, as well as the first edition, a wide audience."Victor Gichev in: Zentralblatt MATH 17/2008 Biographical note: Karl H. Hofmann, TU Darmstadt, Germany; Sidney A. Morris, University of Ballarat, Australien