Cayley transform is a technique to project from Lie algebra to the underlying Lie group. The transform is widely employed as a retraction map for Riemannian optimization. In this talk, we consider the applicability of the Cayley transform of the general Lie group and its representations, which is closely related to the power span property of the representation of Lie algebra. For semisimple Lie algebra, the weights of the representation can be characterized in detail, under the assumption of power span property.