Local automorphisms of n-dimensional naturally graded quasi-filiform Leibniz algebra of type I

Document Type : Research Paper

Authors

1 V. I. Romanovskiy Institute of Mathematics, University Street 9, Tashkent, 100174, Uzbekistan and Chirchiq State Pedagogical University, Amir Temur Street 104, 111700, Uzbekistan.

2 V. I. Romanovskiy Institute of Mathematics, University Street 9, Tashkent, 100174, Uzbekistan and Urgench State University, H. Alimdjan street 14, Urgench, 220100, Uzbekistan.

Abstract

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.

Keywords

References

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Algebraic Structures and Their Applications
Volume 11, Issue 1
February 2024
Pages 11-24

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