Local 1/2-derivation on of n-dimensional naturally graded quasi-filiform Leibniz algebra of type I.

For a given Lie algebra L, the main problem about local 1 2 -derivations is to prove that they automatically become an 1 2 -derivation or to give examples of local 1 2 -derivation of L, which are not 1 2 -derivation. In this paper, we investigate local 1 2 -derivations on quasi-filiform Leibniz algebras. It is proved that quasi-filiform Leibniz algebras of type I, as a rule, admit a local 1 2 -derivation which is not 1 2 -derivation. [ABSTRACT FROM AUTHOR]