2-local derivations on the perfect Lie algebras Lm

Articles in Press

Document Type : Research Paper

Authors

1 Ch. Abdirov 1, Department of Mathematics, Karakalpak State University, Nukus 230113, Uzbekistan, and V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, University Street, 9, Olmazor district, Tashkent, 100174, Uzbekistan

2 School of Mathematics, Jilin University, Changchun, 130012, China, and V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, University Street, 9, Olmazor district, Tashkent, 100174, Uzbekistan.

3 V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Univesity Street, 9, Olmazor district, Tashkent, 100174, Uzbekistan, and Department of Algebra and Mathematical Engineering, Urgench State University, H. Alimdjan Street, 14, Urgench 220100, Uzbekistan

Abstract

The notions of a 2-local derivation for Lie algebras are defined similarly to the associative case. It is clear that every derivation of a Lie algebra L is a 2-local derivation. For a given Lie algebra L, the main problem concerning these notions is to prove that every 2-local derivation automatically becomes a derivation or to give examples of Lie algebras which admit 2-local derivations which are not derivations. The present paper is devoted to study 2-local derivations on the perfect Lie algebra Lm. We prove that every 2-local derivation on this algebra is a derivation.

Keywords

References

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Algebraic Structures and Their Applications

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Available Online from 08 February 2025

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