The structure of compact groups

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The subject of compact groups is essential in algebra, topology, functional analysis, and theoretical physics. This book serves as both a textbook for upper-level graduate courses and a resource for research specialists needing to apply the structure and representation theory of compact groups. It begins with an accessible introduction to compact groups and their representation theory, followed by comprehensive courses on linear Lie groups, compact Lie groups, and locally compact abelian groups. Additional chapters cover abelian groups and category theory. The focus is on the structure theory of compact groups that are not necessarily finite-dimensional or commutative, 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 (1998) and the second (2006) received positive reviews and have been widely cited in education and research. This new edition addresses typographical errors, refines concepts, and enhances content based on advancements in research on compact groups. The authors incorporated feedback from readers to clarify certain aspects and expanded the reference list to include recent relevant publications.