2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71561We 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 $\SO(7)$.14 pagesDifferential Geometry53A30; 53C29text