  We present a classification of conformally-invariant three-point tensor
structures in $d$ dimensions that parallels the classification of
three-particle scattering amplitudes in $d+1$ dimensions. Using a set of
canonically-normalized weight-shifting operators, we construct a basis of
three-point structures involving conserved currents or stress tensors and
non-conserved spinning operators, directly from their amplitude counterparts.
As an application, we also examine the conformal block expansion of the
four-point functions of external currents and stress tensors in this amplitude
basis. Our results can be useful for conformal bootstrap applications involving
spinning correlators as well as Witten diagram computations in anti-de Sitter
space.
