Almost inner derivations of two-step nilpotent Leibniz algebras

We investigate almost inner derivations of Leibniz algebras, a notion recently introduced by Bumrungkit, Navisej, Phanfai, and Pongprasert. We prove that every nilpotent Leibniz algebra whose derived algebra coincides with its Leibniz kernel admits no non-inner almost inner derivations. Furthermore, for nilpotent Leibniz algebras with one-dimensional derived algebra, we establish an explicit formula for the dimension of the space of almost inner derivations. We classify all two-step nilpotent non-Lie Leibniz algebras of dimension at most five with one-dimensional Leibniz kernel and explicitly determine their almost inner derivations. As a consequence, we show that every such algebra admits no non-inner almost inner derivations and provide an explicit matrix description of its almost inner derivations.