Local and 2-local automorphisms of some solvable Leibniz algebras

TL;DR

This paper proves that local and 2-local automorphisms of certain solvable Leibniz algebras with specific nilradicals are actually automorphisms, extending understanding of their automorphism structure.

Contribution

It establishes that local and 2-local automorphisms are genuine automorphisms for a class of solvable Leibniz algebras with particular nilradicals.

Findings

Local automorphisms are automorphisms in the studied algebras.

2-local automorphisms are also automorphisms in these cases.

Results extend automorphism characterizations to broader algebra classes.

Abstract

In this paper we prove that any local automorphism on the solvable Leibniz algebras with null-filiform and naturally graded non-Lie filiform nilradicals, whose dimension of complementary space is maximal is an automorphism. Furthermore, the same problem concerning 2-local automorphisms of such algebras is investigated and we obtain the analogously results for 2-local automorphisms.