Conformal Holonomy of Bi-invariant Metrics
نویسنده
چکیده
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).
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