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<p>This paper investigates (tri)dendriform conformal algebras, quadri-conformal algebras, NS-conformal algebras, and Rota–Baxter operators within the framework of BiHom-associative conformal algebras. A comprehensive characterization of BiHom-(tri)dendriform conformal algebras in terms of conformal bimodules is presented. It is demonstrated that BiHom-NS-conformal algebras can be constructed from NS-conformal algebras using two structural maps and can also be derived from BiHom-(tri)dendriform conformal algebras. Furthermore, a strong connection between BiHom-NS-conformal algebras and H-twisted Rota–Baxter operators is established. The study reveals a close relationship between BiHom-quadri conformal algebras and BiHom-dendriform conformal algebras. Additionally, the foundational theory of Rota–Baxter systems, a recent generalization of Rota–Baxter operators, is introduced for BiHom-associative and BiHom-dendriform conformal algebras, demonstrating intricate interrelations among these structures. Finally, a connection between BiHom-quadri conformal algebras and Rota–Baxter systems for BiHom-dendriform conformal algebras is explored. These algebraic structures, including (tri)dendriform algebras, Rota–Baxter operators, and NS-algebras, hold significant potential for applications in physics, particularly in quantum field theory.</p>

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Rota–Baxter Operators and Loday-Type Algebras on the BiHom-Associative Conformal Algebras

  • 期刊论文

  • 发表日期：

    2025年1月29日

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  • Sania Asif,
  • Yao Wang

摘要

This paper investigates (tri)dendriform conformal algebras, quadri-conformal algebras, NS-conformal algebras, and Rota–Baxter operators within the framework of BiHom-associative conformal algebras. A comprehensive characterization of BiHom-(tri)dendriform conformal algebras in terms of conformal bimodules is presented. It is demonstrated that BiHom-NS-conformal algebras can be constructed from NS-conformal algebras using two structural maps and can also be derived from BiHom-(tri)dendriform conformal algebras. Furthermore, a strong connection between BiHom-NS-conformal algebras and H-twisted Rota–Baxter operators is established. The study reveals a close relationship between BiHom-quadri conformal algebras and BiHom-dendriform conformal algebras. Additionally, the foundational theory of Rota–Baxter systems, a recent generalization of Rota–Baxter operators, is introduced for BiHom-associative and BiHom-dendriform conformal algebras, demonstrating intricate interrelations among these structures. Finally, a connection between BiHom-quadri conformal algebras and Rota–Baxter systems for BiHom-dendriform conformal algebras is explored. These algebraic structures, including (tri)dendriform algebras, Rota–Baxter operators, and NS-algebras, hold significant potential for applications in physics, particularly in quantum field theory.