Local automorphisms of some p-filiform Leibniz algebras

In the present paper automorphisms and local automorphisms of p-filiform Leibniz algebras are studied. Namely, a common form of the matrix of automorphisms and local automorphisms of these algebras is clarified. It turns out that the common form of the matrixof an automorphism on these algebras does not coincide with the local automorphism’s matricescommon form on these algebras. Therefore, these p-filiform Leibniz algebras have local automorphisms that are not automorphisms.