The structure of compact groups

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This book addresses compact groups, a topic often referenced in algebra, topology, functional analysis, and theoretical physics. It serves as both a textbook for advanced graduate courses and a resource for researchers applying the structure and representation theory of compact groups. Beginning with a gentle introduction, it covers linear Lie groups, compact Lie groups, and locally compact abelian groups. The main focus, however, is on the structure theory of infinite-dimensional compact groups, which may not be commutative and are free from weight restrictions or dimensional limits. The text employs infinite-dimensional Lie algebras and the exponential function of arbitrary compact groups. The first edition, released in 1998, received positive reviews and has been widely cited in educational and research contexts. This new edition has corrected typographical errors and minor inaccuracies, with various sections edited and improved. Additionally, new material has been included to reflect ongoing research developments. Throughout the revisions, the integrity of the original section numbering has been maintained, ensuring that citations from the first edition remain valid for users of this updated version.