U. Mamadaliyev, A. Sattarov, B. Yusupov, “Local and $2$-local $\frac12$-derivations of solvable Leibniz algebras”, Eurasian Math. J., 16:2 (2025), 42

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Eurasian Mathematical Journal, 2025, Volume 16, Number 2, Pages 42–54
DOI: https://doi.org/10.32523/2077-9879-2025-16-2-42-54 (Mi emj531)

This article is cited in 2 scientific papers (total in 2 papers)

Local and $2$-local $\frac12$-derivations of solvable Leibniz algebras

U. Mamadaliyev^a, A. Sattarov^b, B. Yusupov^cd

^a Department of Mathematics, Namangan State University, Uychi St, 316 160119, Namangan, Republic of Uzbekistan
^b Department of Management and Digitization, University of Business and Science, Beshkapa St, 111, 160119, Namangan, Republic of Uzbekistan
^c Department of Algebra and Mathematical Engineering, Urgench State University, H. Alimdjan St, 14, 220100, Urgench, Republic of Uzbekistan
^d V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Univesity St, 9, Olmazor district, 100174, Tashkent, Republic of Uzbekistan

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DOI: https://doi.org/10.32523/2077-9879-2025-16-2-42-54

Abstract: We show that any local $\frac12$-derivation on solvable Leibniz algebras with model or abelian nilradicals, whose dimensions of complementary spaces are maximal, is a $\frac12$-derivation. We show that solvable Leibniz algebras with abelian nilradicals, which have $1$-dimensional complementary spaces are $\frac12$-derivations. Moreover, a similar problem concerning $2$-local $\frac12$-derivations of such algebras is investigated.

Keywords and phrases: Leibniz algebras, solvable algebras, nilpotent algebras, $\frac12$-derivation, local $\frac12$-derivation, $2$-local $\frac12$-derivation.

Received: 30.10.2023

Document Type: Article

MSC: 17A32, 17B30, 17B10

Language: English

Citation: U. Mamadaliyev, A. Sattarov, B. Yusupov, “Local and $2$-local $\frac12$-derivations of solvable Leibniz algebras”, Eurasian Math. J., 16:2 (2025), 42–54

Citation in format AMSBIB

\Bibitem{MamSatYus25}

\by U.~Mamadaliyev, A.~Sattarov, B.~Yusupov

\paper Local and $2$-local $\frac12$-derivations  of solvable Leibniz algebras

\jour Eurasian Math. J.

\yr 2025

\vol 16

\issue 2

\pages 42--54

\mathnet{http://mi.mathnet.ru/emj531}

\crossref{https://doi.org/10.32523/2077-9879-2025-16-2-42-54}

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