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Expanding maps on infra-nilmanifolds of homogeneous type

In this paper we investigate expanding maps on infra-nilmanifolds. Such manifolds are obtained as a quotient E\L, where L is a connected and simply connected nilpotent Lie group and E is a torsion-free uniform discrete subgroup of L×C, with C a compact subgroup of Aut(L). We show that if the Lie algebra of L is homogeneous (i.e., graded and generated by elements of degree 1), then the corresponding infra-nilmanifolds admit an expanding map. This is a generalization of the result of H. Lee and K. B. Lee, who treated the 2-step nilpotent case.