Blending algebra, analysis, and topology, the study of compact Lie groups is one of the most beautiful areas of mathematics and a key stepping stone to the theory of general Lie groups. Assuming no prior knowledge of Lie groups, this book covers the structure and representation theory of compact Lie groups.

Provides an approach that minimizes advanced prerequisites Self-contained and systematic exposition requiring no previous exposure to Lie theory Advances quickly to the Peter-Weyl Theorem and its corresponding Fourier theory Streamlined Lie algebra discussion reduces the differential geometry prerequisite and allows a more rapid transition to the classification and construction of representations Exercises sprinkled throughout the text

Inhalt
Compact Lie Groups.- Representations.- HarmoniC Analysis.- Lie Algebras.- Abelian Lie Subgroups and Structure.- Roots and Associated Structures.- Highest Weight Theory.