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<p>A Lie conformal algebra <i>L</i> is defined as a ℂ[∂]-module (∂ is an indeterminate), endowed with a ℂ-linear map <i>L</i> ⊗ <i>L</i> → ℂ[<i>λ</i>] ⊗ <i>L, a</i> ⊗ <i>b</i> → [<i>a</i><sub><i>λ</i></sub><i>b</i>] satisfying axioms similar to those of Lie algebra. Then Bakalov, D’Andrea and Kac introduced the notion of Lie <i>H</i>-pseudoalgebras by replacing the above polynomial algebra ℂ[∂] with any cocommutative Hopf algebra <i>H</i>. We first classify solvable Lie <i>H</i>-pseudoalgebras of rank two. Then we consider the Rota-Baxter <i>H</i>-operators on such Lie <i>H</i>-pseudoalgebras. Finally, we study the relationship between Rota-Baxter <i>H</i>-operators on Lie <i>H</i>-pseudoalgebra and Rota-Baxter operators on its annihilation algebra.</p>

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Lie H-pseudoalgebras with Rota-Baxter H-operators

  • 期刊论文

  • 发表日期：

    2025年9月28日

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  • Botong Gai,
  • Shuanhong Wang

摘要

A Lie conformal algebra L is defined as a ℂ[∂]-module (∂ is an indeterminate), endowed with a ℂ-linear map L ⊗ L → ℂ[λ] ⊗ L, a ⊗ b → [aλb] satisfying axioms similar to those of Lie algebra. Then Bakalov, D’Andrea and Kac introduced the notion of Lie H-pseudoalgebras by replacing the above polynomial algebra ℂ[∂] with any cocommutative Hopf algebra H. We first classify solvable Lie H-pseudoalgebras of rank two. Then we consider the Rota-Baxter H-operators on such Lie H-pseudoalgebras. Finally, we study the relationship between Rota-Baxter H-operators on Lie H-pseudoalgebra and Rota-Baxter operators on its annihilation algebra.