Invariant conformal Killing forms on almost abelian Lie groups

We describe completely conformal Killing or conformal Killing-Yano (CKY) p-forms on almost abelian metric Lie algebras. In particular we prove that if a n-dimensional almost abelian metric Lie algebra admits a non-parallel CKY p-form, then $p=1$ or $p=n-1$. In other words, any CKY p-form on a metric almost abelian Lie algebra is parallel for 2≤ p≤ n-2. Moreover, we characterize almost abelian Lie algebras admitting non-parallel CKY p-forms, and we classify all Lie algebras with this property up to dimension $5$, distinguishing also those cases where the associated simply connected Lie group admits lattices.