Two-step nilpotent Leibniz algebras

In this paper we give a complete classification of two-step nilpotent Leibniz algebras in terms Kronecker modules associated with pairs bilinear forms. particular, describe the complex and real case indecomposable Heisenberg as generalization classical $(2n+1)-$dimensional Lie algebra $\mathfrak{h}_{2n+1}$. Then use - local racks correspondence proposed by S. Covez to show that have always global integration. As an application, integrate one-dimensional commutator ideal. We also every quandle integrating is induced conjugation group group.