Polynomial invariants for 3-dimensional Leibniz algebras

Abstract: For every 3-dimensional non-Lie Leibniz algebras over complex numbers we describe the algebra of polynomial invariants and the group of automorphisms. As a consequence, we establish that two non-nilpotent 3-dimensional non-Lie Leibniz algebras can be distinguished by means of the traces of degrees $\leqslant2$ and the dimensions of groups of automorphisms.