Semisimple Lie Groups

  • Joachim HilgertEmail author
  • Karl-Hermann Neeb
Part of the Springer Monographs in Mathematics book series (SMM)


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.


Root Decomposition Iwasawa Decomposition Cartan Decomposition Involutive Automorphism Cartan Involution 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of PaderbornPaderbornGermany
  2. 2.Department of MathematicsFriedrich-Alexander Universität Erlangen-NürnbergErlangenGermany

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