Local automorphisms on naturally graded filiform Leibniz algebra

In this paper, we investigate automorphisms and local automorphisms on naturally graded filiform Leibniz algebras. We obtain explicit descriptions of automorphisms and local automorphisms of these algebras. In connection with the Ayupov–Elduque–Kudaybergenov problem, we study the structure of the set of all local automorphisms. Moreover, we prove that the set of all local automorphisms forms a finitedimensional Lie group with respect to the composition of mappings. The obtained results contribute to the study of local mappings on non-associative algebras and provide a structural description of local automorphisms on naturally graded filiform Leibniz algebras.

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