Jobir Adashev - V. I. Romanovskiy Institute of Mathematics, University Street ۹, Tashkent, ۱۰۰۱۷۴, Uzbekistan and Chirchiq State Pedagogical University, Amir Temur Street ۱۰۴, ۱۱۱۷۰۰, Uzbekistan.
Bakhtiyor Yusupov - V. I. Romanovskiy Institute of Mathematics, University Street ۹, Tashkent, ۱۰۰۱۷۴, Uzbekistan and Urgench State University, H. Alimdjan street ۱۴, Urgench, ۲۲۰۱۰۰, Uzbekistan.

The notions of a local automorphism for Lie algebras are defined as similar to the associative case. Every automorphism of a Lie algebra \mathcal{L} is a local automorphism. For a given Lie algebra \mathcal{L}, the main problem concerning these notions is to prove that they automatically become an automorphism or to give examples of local automorphisms of \mathcal{L}, which are not automorphisms. In this paper, we study local automorphisms on quasi-filiform Leibniz algebras. It is proved that quasi-filiform Leibniz algebras of type I, as a rule, admit local automorphisms which are not automorphisms.

Automorphisms, Leibniz algebras, Local automorphisms, Nilpotent algebras