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

## TL;DR

This paper characterizes 2-step nilpotent Lie groups that admit non-degenerate left invariant Killing-Yano 2-forms, showing they are precisely the complex Lie groups, with a focus on those from connected graphs.

## Contribution

It identifies the specific class of 2-step nilpotent Lie groups supporting non-degenerate Killing-Yano 2-forms and describes the structure of these forms in graph-derived cases.

## Key findings

- Only complex Lie groups among 2-step nilpotent groups admit such forms.
- The space of invariant Killing-Yano 2-forms is one-dimensional for graph-derived groups.
- Non-degenerate forms are exclusive to complex Lie groups in this setting.

## Abstract

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.