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<p>Let <i>X</i> be a locally finite partially ordered set, let <i>K</i> be a field of characteristic not 2, and let <i>I</i>(<i>X</i>,&#xa0;<i>K</i>) be the incidence algebra of <i>X</i> over <i>K</i>. We prove that every Jordan <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-derivation of <i>I</i>(<i>X</i>,&#xa0;<i>K</i>) is the sum of an inner <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-derivation and a transposed Jordan <InlineEquation ID="IEq6"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-derivation. We also provide examples of Jordan <InlineEquation ID="IEq7"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-derivations that are neither <InlineEquation ID="IEq8"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-derivations nor inner <InlineEquation ID="IEq9"> <EquationSource Format="TEX">\(*\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mrow /> <mo>∗</mo> </mrow> </math></EquationSource> </InlineEquation>-derivations.</p>

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Jordan \(*\)-Derivations of Incidence Algebras

  • 期刊论文

  • 发表日期：

    2026年7月28日

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  • Liuqing Yang,
  • Jiayi Han

摘要

Let X be a locally finite partially ordered set, let K be a field of characteristic not 2, and let I(X, K) be the incidence algebra of X over K. We prove that every Jordan \(*\) ∗ -derivation of I(X, K) is the sum of an inner \(*\) ∗ -derivation and a transposed Jordan \(*\) ∗ -derivation. We also provide examples of Jordan \(*\) ∗ -derivations that are neither \(*\) ∗ -derivations nor inner \(*\) ∗ -derivations.