Homogeneous locally symmetric regions in homogeneous spaces associated with semisimple Jordan algebras

The search for such regions is equivalent to the search for certain subalgebras in the Lie algebra of the group of transformations of a homogeneous space. The latter problem is solved for homogeneous spaces compared in a definite way with semisimple Jordan algebras. By a sequence of reductions, the problem is reduced to finding certain linear mappings of the Jordan algebra into itself. Conditions characterizing these mappings are obtained. Geometric consequences are given.
Bibliography: 10 titles.