Polynomial invariants for 3-dimensional Leibniz algebras

For each 3-dimensional non-Lie Leibniz algebra over the complex numbers, we describe the algebra of polynomial invariants and determine its group of automorphisms. As a consequence, we establish that any two non-nilpotent 3-dimensional non-Lie Leibniz algebras can be distinguished by the traces of degrees $⩽2$ and by the dimensions of their automorphism groups.