A general construction of conformally covariant tridifferential operators

We construct a large family of conformally covariant tridifferential operators as tangential operators in the Fefferman–Graham ambient space. Our construction is analogous to the linear and bilinear constructions of Graham–Jenne–Mason–Sparling and Case–Lin–Yuan, respectively. We also show that the symmetrization of our ambient operators are formally self-adjoint when acting on densities of the correct weight.