  Consider the smooth sections of the tangent bundle of a reductive homogeneous
space. This is a vector space over the field of real numbers. The canonical
connection acts as a linear binary operator on this vector space, making it an
algebra. If we include another binary operator defined as the negative of the
torsion, the resulting algebraic structure is a post-Lie-Yamaguti algebra. This
structure is closely related to Lie-Yamaguti algebras.
