Invariant conformal Killing forms on almost abelian Lie groups

Abstract

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