Almost inner derivations of finite-dimensional simple Leibniz algebras

Authors

  • Tuuelbay Kurbanbaev Karakalpak State University, Nukus, Uzbekistan, V. I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent, Uzbekistan

DOI:

https://doi.org/10.3842/umzh.v77i11.8997

Keywords:

Lie algebra, Leibniz algebra, simple Lie algebra, simple Leibniz algebra, derivation, inner derivation, almost inner derivation.

Abstract

UDC 512.5

We study almost inner derivations of finite-dimensional simple Leibniz algebras. First, we examine almost inner derivations of the simple Leibniz algebra $\mathfrak{sl}_2\ltimes\mathcal{I}$  and prove that every  derivation of this kind is inner. Furthermore, we analyze almost inner derivations of other simple Leibniz algebras and show that the existence of almost inner derivations that are not inner is possible only in cases other than $\mathfrak{sl}_2.$

References

The full version of this paper will be published in Ukrainian Mathematical Journal, Vol. 77, No. 11, 2025.

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Published

24.10.2025

Issue

Vol. 77 No. 11 (2025)

Section

Research articles

License

Copyright (c) 2025 Tuuelbay Kurbanbaev

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite

Kurbanbaev, Tuuelbay. “Almost Inner Derivations of Finite-Dimensional Simple Leibniz Algebras”. Ukrains’kyi Matematychnyi Zhurnal, vol. 77, no. 11, Oct. 2025, p. 697, https://doi.org/10.3842/umzh.v77i11.8997.