We discuss in this paper the conformal geometry of bi-invariant metrics on compact semisimple Lie groups. For this purpose we develop a conformal Cartan calculus adapted to this problem. In particular, we derive an explicit formula for the holonomy algebra of the normal conformal Cartan connection of a bi-invariant metric. As an example, we apply this calculus to the group $\SO(4)$. Its conformal holonomy group is calculated to be $\SO(7)$.
An introduction to conformal geometry and tractor calculus, with a view to applications in general relativity
A priori estimates and existence for a class of fully nonlinear elliptic equations in conformal geometry
Invariant Prolongation of BGG-Operators in Conformal Geometry
![QR code for arXiv:math/0406299 [math.DG]](http://oss.arxitics.com/images/favicon.svg)