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<p>The present paper is a continuation of [Comm. Algebra, 2014, 42(5): 2195–2212], where we constructed the Drinfeld double of braided infinitesimal Hopf algebras (i.e., infinitesimal Hopf algebras in the Yetter–Drinfeld category <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({}_{H}^{H}{\mathcal{Y}}{\mathcal{D}}\)</EquationSource> </InlineEquation>). In this paper we show the Drinfeld double of braided Lie bialgebras (i.e., Lie bialgebras in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({}_{H}^{H}{\mathcal{Y}}{\mathcal{D}}\)</EquationSource> </InlineEquation>) and present the Drinfeld double of Sl<sub>2</sub> in Yetter–Drinfeld categories over the group algebra <i>H</i> = <i>kG</i>. Finally, we consider the relation between the Drinfeld double of braided infinitesimal Hopf algebras and braided Lie bialgebras.</p>

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Drinfeld Double of Braided Lie Bialgebras and Braided Infinitesimal Hopf Algebras

  • 期刊论文

  • 发表日期：

    2026年7月5日

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  • Shengxiang Wang,
  • Ruoyu Wang,
  • Xiaohui Zhang

摘要

The present paper is a continuation of [Comm. Algebra, 2014, 42(5): 2195–2212], where we constructed the Drinfeld double of braided infinitesimal Hopf algebras (i.e., infinitesimal Hopf algebras in the Yetter–Drinfeld category \({}_{H}^{H}{\mathcal{Y}}{\mathcal{D}}\) ). In this paper we show the Drinfeld double of braided Lie bialgebras (i.e., Lie bialgebras in \({}_{H}^{H}{\mathcal{Y}}{\mathcal{D}}\) ) and present the Drinfeld double of Sl2 in Yetter–Drinfeld categories over the group algebra H = kG. Finally, we consider the relation between the Drinfeld double of braided infinitesimal Hopf algebras and braided Lie bialgebras.