Conformal maps in higher dimensions and derived geometry
Algebraic Geometry
2021-02-24 v1 High Energy Physics - Theory
Differential Geometry
Abstract
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.
Cite
@article{arxiv.2102.11507,
title = {Conformal maps in higher dimensions and derived geometry},
author = {Mikhail Kapranov},
journal= {arXiv preprint arXiv:2102.11507},
year = {2021}
}
Comments
19 pages