The Connection Algebra of Reductive Homogeneous Spaces

The connection algebra of a reductive homogeneous space is called an invariant connection algebra. This is an algebra that is closely related to Lie-Yamaguti algebras. In this article we describe this structure and provide a basis for the free invariant connection algebra. We also give a summary of the less complicated connection algebras that occur when the torsion or the curvature is vanishing.