  By Liouville's theorem, in dimensions 3 or more conformal transformations
form a finite-dimensional group, an apparent drastic departure from the
2-dimensional case. We propose a derived enhancement of the conformal Lie
algebra which is an infinite-dimensional dg-Lie algebra incorporating not only
symmetries but also deformations of the conformal structure. Our approach is
based on (derived) deformation theory of the ambitwistor space of complex
null-geodesics.
