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In this article we show that the only 2-step nilpotent Lie groups which carry a non-degenerate left invariant Killing–Yano 2-form are the complex Lie groups. In the case of 2-step nilpotent complex Lie groups arising from connected graphs, we prove that the space of left invariant Killing–Yano 2-forms is one-dimensional.

Killing–Yano 2-forms on 2-step nilpotent Lie groups