Homogeneous spaces with invariant projectively flat affine connections

We characterize invariant projectively at affine connections in terms of affine representations of Lie algebras, and show that a homogeneous space admits an invariant projectively at affine connection if and only if it has an equivariant centro-affine immersion. We give a correspondence between semi-simple symmetric spaces with invariant projectively at affine connections and central-simple Jordan algebras.