ON A CONNECTION USED IN DEFORMATION QUANTIZATION.

We show that the connection used by Bordemann, Neumaier and Waldmann to construct the Fedosov standard ordered star product on the cotangent bundle of a Riemannian manifold is obtained by symplectification of the complete lift of the corresponding Levi-Civitá connection, in the sense of Yano and Patterson. In terms of local coordinates, this was already shown earlier by Plebanski, Przanowski and Turrubiates. In the final part, we comment on the usefulness of this connection in the context of homological reduction of deformation quantized models. [ABSTRACT FROM AUTHOR]