Local and 2-Local Automorphisms of solvable Leibniz algebras with Abelian and Model Nilradicals 1

Abstract

In the paper, we describe the automorphisms on the solvable Leibniz algebras with the model or abelian nilradicals, whose complementary spaces are equal to two and one, respectively. We show that any local automorphism on a solvable Leibniz algebra with  model nilradical of maximal codimension is an automorphism. We show that solvable Leibniz algebras with abelian nilradicals, which  have 1-dimension complementary space, admit local automorphisms which are not automorphisms. Moreover, similar problems  concerning 2-local automorphisms of such algebras are investigated. We give examples of solvable Leibniz algebras in which 2-local  automorphisms are automorphisms and examples of such algebras which admit 2-local automorphisms which are not automorphisms.