In this chapter we begin our discussion of the classification theory of compact connected Lie groups. Our aim is to introduce the main ideas involved and eventually to describe the outcome of this classification in terms of root systems and Dynkin diagrams. The reader interested in seeing more details might usefully consult some of the books [1, 2, 4, 7, 13, 14, 26] which focus on various aspects of this theory.
KeywordsNormal Subgroup Weyl Group Maximal Torus Adjoint Action Matrix Group
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