Fino-Vezzoni conjecture on Lie algebras with abelian ideals of codimension two

In this paper, we confirm the Fino-Vezzoni Conjecture for unimodular Lie algebras which contain abelian ideals of codimension two, a natural generalization to the class of almost abelian Lie algebras. This provides new evidence towards the validity of the conjecture on a very special type of $3$-step solvmanifolds.