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<p>In this paper, we consider perm algebras equipped with a derivation <i>d</i> and introduce a new operation <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41980_2025_981_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="103" /> </InlineMediaObject> <EquationSource Format="TEX">\(a \succ b = d(a) b\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>a</mi> <mo>≻</mo> <mi>b</mi> <mo>=</mo> <mi>d</mi> <mo stretchy="false">(</mo> <mi>a</mi> <mo stretchy="false">)</mo> <mi>b</mi> </mrow> </math></EquationSource> </InlineEquation>. Using this new operation on differential perm algebra, we construct a linear basis of the free Novikov dialgebra. We also describe a complete list of identities that hold on every differential perm algebra relative to the operation <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="41980_2025_981_Article_IEq2.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="17" /> </InlineMediaObject> <EquationSource Format="TEX">\(\succ \)</EquationSource> <EquationSource Format="MATHML"><math> <mo>≻</mo> </math></EquationSource> </InlineEquation>.</p>

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Novikov Dialgebras and Perm Algebras

  • 期刊论文

  • 发表日期：

    2025年7月14日

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  • Bauyrzhan Sartayev,
  • Askar Dzhumadil’daev,
  • Farukh Mashurov

摘要

In this paper, we consider perm algebras equipped with a derivation d and introduce a new operation \(a \succ b = d(a) b\) a ≻ b = d ( a ) b . Using this new operation on differential perm algebra, we construct a linear basis of the free Novikov dialgebra. We also describe a complete list of identities that hold on every differential perm algebra relative to the operation \(\succ \) ≻ .