Left invariant Finsler metrics on Lie groups provide an important class of Finsler manifolds. In this paper, we prove several properties of the Ricci curvatures of such spaces. For example, if all the Ricci curvatures are nonnegative, then the underlying Lie group must be unimodular. If the Lie group is noncommutative and nilpotent, then there must be three directions whose Ricci curvature is positive, negative and zero, respectively. This result gives a negative answer to a question of S.-S. Chern.
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