Polynomial invariants for three-dimensional Leibniz algebras

Abstract For each three-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 three-dimensional non-Lie Leibniz algebras can be distinguished by the traces of degrees 2 and by the dimensions of their automorphism groups.