local automorphisms of n-dimensional naturally graded quasi-filiform leibniz algebra of type i

The notions of a local automorphism for lie algebras are defined as similar to the associative case. every automorphism of a lie algebra l is a local automorphism. for a given lie algebra l, the main problem concerning these notions is to prove that they automatically become an automorphism or to give examples of local automorphisms of 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.