Abstract
This chapter consists of a concise exposition of the structure and classification theories of compact Lie groups and their representations from the geometric viewpoint of transformation groups. An explicit and neat understanding of the orbit structure of the adjoint action of a compact Lie group G plays a central role in the classification theory developed by É. Cartan and H. Weyl. This more geometric approach is actually more natural and straightforward than the usual Lie-algebra-theoretical approach. Furthermore, such an approach will also provide us with valuable examples and insight for later investigation of topological transformation groups.
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© 1975 Springer-Verlag Berlin Heidelberg
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Hsiang, W.Y. (1975). Structural and Classification Theory of Compact Lie Groups and Their Representations. In: Cohomology Theory of Topological Transformation Groups. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 85. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-66052-8_2
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DOI: https://doi.org/10.1007/978-3-642-66052-8_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-66054-2
Online ISBN: 978-3-642-66052-8
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