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<p>In this work we study how to extend a partial action of a Hopf Algebra <i>A</i> on an algebra <i>R</i> to a partial action of a Hopf-Ore extension of <i>A</i> on <i>R</i>. As consequence, we exhibit all partial actions of rank one Hopf algebras (in particular, generalized Taft algebras and Radford algebras) on an algebra <i>R</i> for which <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(g \cdot 1_R\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>g</mi> <mo>·</mo> <msub> <mn>1</mn> <mi>R</mi> </msub> </mrow> </math></EquationSource> </InlineEquation> is either <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(1_R\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mn>1</mn> <mi>R</mi> </msub> </math></EquationSource> </InlineEquation> or 0.</p>

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On Partial Actions of Hopf-Ore Extensions

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年6月25日

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  • Leonardo Duarte Silva,
  • João Matheus Jury Giraldi,
  • Grasiela Martini

摘要

In this work we study how to extend a partial action of a Hopf Algebra A on an algebra R to a partial action of a Hopf-Ore extension of A on R. As consequence, we exhibit all partial actions of rank one Hopf algebras (in particular, generalized Taft algebras and Radford algebras) on an algebra R for which \(g \cdot 1_R\) g · 1 R is either \(1_R\) 1 R or 0.