The Structure of Compact Groups : : A Primer for Students - A Handbook for the Expert / / Karl H. Hofmann, Sidney A. Morris.

• Superior document: Title is part of eBook package: De Gruyter DG Studies in Mathematics eBook-Package
• VerfasserIn: Hofmann, Karl H.,; Morris, Sidney A.,
• Place / Publishing House: Berlin ;, Boston : : De Gruyter, , [2008]; ©2006
• Year of Publication: 2008
• Edition: 2nd rev. and augmented ed.
• Language: English
• Series: De Gruyter Studies in Mathematics , 25
• Physical Description: 1 online resource (858 p.)

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 "ed 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.

Table of Contents

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