Outer Automorphism Groups of Complex and Real Simple Lie Algebras
The preceding interpretation of outer automorphisms as symmetries of a Dynkin diagram follows from the general fact, that for a complex or real simple Lie algebra, the automorphism group is a semidirect product of and, i.e., the short exact sequence
splits. In the complex simple case, this is a classical result, whereas for real simple Lie algebras, this fact has been proven as recently as 2010.
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