A general construction of conformally covariant tridifferential operators

TL;DR

This paper introduces a broad family of conformally covariant tridifferential operators constructed via ambient space methods, extending previous linear and bilinear frameworks and establishing their self-adjointness properties.

Contribution

It provides a new general construction of conformally covariant tridifferential operators using ambient space techniques, expanding the existing linear and bilinear operator frameworks.

Findings

Constructed a large family of conformally covariant tridifferential operators.

Proved symmetrized operators are formally self-adjoint on densities of appropriate weight.

Extended previous linear and bilinear operator constructions to a more general setting.

Abstract

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.