The maximal-complement conjecture for local and 2-local automorphisms of solvable Leibniz algebras

Let $L$ be a solvable Leibniz algebra with a given nilradical, and suppose that the dimension of a complementary space to the nilradical is maximal. Maximal-complement conjecture. Every local automorphism and every 2-local automorphism of $L$ is an automorphism. This conjecture proposes a common extension of the automorphism results established in the paper for particular solvable Leibniz algebras with null-filiform and naturally graded non-Lie filiform nilradicals; the general case remains open.