The examples of class A are completely described by the classification of noncompact simply connected real simple Lie groups. For non-compact type, "G" is such a group and "K" is its maximal compact subgroup. Each such example has a corresponding example of compact type, by considering a maximal compact subgroup of the complexification of "G" which contains "K". More directly, the examples of compact type are classified by involutive automorphisms of compact simply connected simple Lie groups "G" (up to conjugation). Such involutions extend to involutions of the complexification of "G", and these in turn classify non-compact real forms of "G".