摘要
Let g be a simple Lie algebra. Let Aut (g) be the group of all automorphisms on g, and let Int (g) be its identity component. The outer automorphism group of g is defined as Aut(g)/Int(g). If g is complex and has Dynkin diagram D, then Aut(g)/Int(g) is isomorphic to Aut( D ). We provide an analogous result for the real case. For g real, we let g be represented by a painted diagram P. Depending on whether the Cartan involution of (g) belongs to Int(g), we show that Aut(g)/Int(g) is isomorphic to Aut( P ) or Aut( P ) × ℤ 2 . This result extends to the outer automorphism groups of all real semisimple Lie algebras.