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Abstract <p>The problem of finding primitive elements of degree two and three in the free Lie algebra of rank three over the field <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11970_2025_7220_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{F}_{3}\)</EquationSource> <!--BMatMGU2570044Mikhalev-m3--> </InlineEquation> is solved. In addition, estimates of the number of primitive elements of degree two with an arbitrary number of generators over the field <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11970_2025_7220_Article_IEq3.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\mathbb{F}_{3}\)</EquationSource> <!--BMatMGU2570044Mikhalev-m4--> </InlineEquation> are obtained.</p>

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Primitive Elements of Free Lie Algebras over the Field \(\boldsymbol{\mathbb{F}_{3}}\)

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • A. A. Mikhalev,
  • K. M. Shipilova

摘要

Abstract

The problem of finding primitive elements of degree two and three in the free Lie algebra of rank three over the field \(\mathbb{F}_{3}\) is solved. In addition, estimates of the number of primitive elements of degree two with an arbitrary number of generators over the field \(\mathbb{F}_{3}\) are obtained.