On semisimple standard compact Clifford-Klein forms

In this paper we give the classification of standard compact Clifford-Klein forms corresponding to triples (g,h,l) such that g = h+l and g is a sum of two absolutely simple ideals. The classification is done using Onishchik's results concerning semisimple decompositions of semisimple Lie algebras. Using this classification we obtain new examples of reductive homogeneous spaces admitting non-standard compact Clifford-Klein forms.