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.

中文翻译：

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

在本文中，我们展示了唯一带有非退化左不变 Killing-Yano 2-形式的两步幂零李群是复李群。在由连通图产生的两步幂零复李群的情况下，我们证明了左不变Killing-Yano 2-形式的空间是一维的。