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<p>We study almost inner derivations of finite-dimensional simple Leibniz algebras. First, we examine almost inner derivations of the simple Leibniz algebra <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathfrak{s}\mathfrak{l}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="fraktur">s</mi> <mi mathvariant="fraktur">l</mi> </mrow> </math></EquationSource> </InlineEquation> ⋉ <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathcal{I}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="script">I</mi> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\mathfrak{s}{\mathfrak{l}}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="fraktur">s</mi> <msub> <mi mathvariant="fraktur">l</mi> <mn>2</mn> </msub> </mrow> </math></EquationSource> </InlineEquation><i>.</i></p>

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Almost Inner Derivations of Finite-Dimensional Simple Leibniz Algebras

  • 期刊论文

  • 发表日期：

    2025年12月17日

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  • Tuuelbay Kurbanbaev

摘要

We study almost inner derivations of finite-dimensional simple Leibniz algebras. First, we examine almost inner derivations of the simple Leibniz algebra \(\mathfrak{s}\mathfrak{l}\) s l ⋉ \(\mathcal{I}\) 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 \(\mathfrak{s}{\mathfrak{l}}_{2}\) s l 2 .