6.8 Summary – Tits–Satake diagrams for non-compact real forms
To summarize the analysis, we provide the Tits–Satake diagrams for all noncompact real forms of all
simple Lie algebras [5, 93]. We do not give explicitly the Tits–Satake diagrams of the compact real
forms as these are simply obtained by painting in black all the roots of the standard Dynkin
Theorem: The simple real Lie algebras are:
- The Lie algebras where is one of the complex simple Lie algebras
, and the compact
real forms of these.
- The classical real Lie algebras of types , , and . These are listed in Table 26.
- The twelve exceptional real Lie algebras, listed in Table 27 (our conventions are due to Cartan).