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 $\mathcal{L}$ is a local automorphism. For a given Lie algebra $\mathcal{L}$, the main problem concerning these notions is to prove that they automatically become an automorphism or to give examples of local automorphisms of $\mathcal{L}$, 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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