A note on mono-covered acts

Let $ L$ be a nilpotent Lie algebra with one-dimensional center, and let $ L $ be a reduced direct product of two subalgebras $ I_1 $ and $ I_2.$ In the present talk, at first, we give some necessary conditions for the capability of $ L. $ As a result, we determine the structure of capable nilpotent Lie algebras with one-dimensional center.