等質系について(II)

The relations between the properties of analytic homogeneous systems on manifolds and those of their tangent Lie triple algebras are investigated in this paper, by using the results obtained in the preceding paper [2]. It is shown that an isomorphism class of Lie triple algebras corresponds to each isomorphism class of simply connected homogeneous systems (Theorem 2.2). After constructing a universal covering system of a homogeneous system (Theorem 3.1), we show the decomposition theorem of simply connected homogeneous systems (Theorem 4.2). Sorne particular cases are treated in which the homogeneous system is reduced to that of a Lie group, or reduced to a symmetric space (Theorems 1.1 and 1 .3).