This article is cited in 2 papers

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

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

a</sup> 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

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.

MSC: 17A32, 17B30, 17B10

Received: 30.10.2023

Language: English

DOI: 10.32523/2077-9879-2025-16-2-42-54