Semisimple Lie Groups
In the preceding chapter, we studied groups with a compact Lie algebra. For these groups, we have seen how to split them into a direct product of a compact and a vector group, how to complement the commutator group by an abelian Lie group, and that all compact Lie groups are linear. We now proceed with our program to obtain similar results for arbitrary Lie groups with finitely many connected components. First, we turn to the important special case of semisimple Lie groups.
KeywordsRoot Decomposition Iwasawa Decomposition Cartan Decomposition Involutive Automorphism Cartan Involution
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