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A Clifford-Wolf translation of a connected Finsler space is an isometry whichmoves each point the sam distance. A Finsler space $(M, F)$ is calledClifford-Wolf homogeneous if for any two point $x_1, x_2\in M$ there is aClifford-Wolf translation $\rho$ such that $\rho(x_1)=x_2$. In this paper, westudy Clifford-Wolf translations of left invariant Randers metrics on compactLie groups. The mian result is that a left invariant Randers metric on aconnected compact simple Lie group is Clifford-Wolf homogeneous if and only ifthe indicatrix of the metric is a round sphere with respect to a bi-invariantRiemannian metric. This presents a large number of examples of non-reversibleFinsler metrics which are Clifford-Wolf homogeneous.

Clifford-Wolf translations of left invariant Randers metrics on compact Lie groups