Ad-invariant metrics on nonnice nilpotent Lie algebras
We proved in previous work that all real nilpotent Lie algebras of dimension up to $10$ carrying an ad-invariant metric are nice. In this paper we show by constructing explicit examples that nonnice irreducible nilpotent Lie algebras admitting an ad-invariant metric exist for every dimension greater than $10$ and every nilpotency step greater than $2$.