On L-dendriform conformal algebras
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914029239271424 |
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| author | Hajjaji, Atef Yuan, Lamei |
| author_facet | Hajjaji, Atef Yuan, Lamei |
| contents | In this paper, we introduce the concept of L-dendriform conformal algebras, which arise naturally from the study of $\mathcal{O}$-operators on left-symmetric conformal algebras and solutions to the conformal $S$-equation. These algebras extend the classical notions of dendriform and left-symmetric conformal algebras, providing a unified algebraic framework for understanding compatible structures in conformal algebra theory. We establish fundamental properties of L-dendriform conformal algebras, explore their relationships with $\mathcal{O}$ -operators, Rota-Baxter operators, and Nijenhuis operators, and demonstrate their connections to dendriform and quadri conformal algebras. Additionally, we investigate compatible $\mathcal{O}$-operators and their induced compatible L-dendriform conformal algebra structures. Our results generalize and unify several existing algebraic structures in conformal algebra theory, offering new insights into their interplay and applications. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07316 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On L-dendriform conformal algebras Hajjaji, Atef Yuan, Lamei Rings and Algebras 17A30, 17B65, 17B69, 17B10, 17B38 In this paper, we introduce the concept of L-dendriform conformal algebras, which arise naturally from the study of $\mathcal{O}$-operators on left-symmetric conformal algebras and solutions to the conformal $S$-equation. These algebras extend the classical notions of dendriform and left-symmetric conformal algebras, providing a unified algebraic framework for understanding compatible structures in conformal algebra theory. We establish fundamental properties of L-dendriform conformal algebras, explore their relationships with $\mathcal{O}$ -operators, Rota-Baxter operators, and Nijenhuis operators, and demonstrate their connections to dendriform and quadri conformal algebras. Additionally, we investigate compatible $\mathcal{O}$-operators and their induced compatible L-dendriform conformal algebra structures. Our results generalize and unify several existing algebraic structures in conformal algebra theory, offering new insights into their interplay and applications. |
| title | On L-dendriform conformal algebras |
| topic | Rings and Algebras 17A30, 17B65, 17B69, 17B10, 17B38 |
| url | https://arxiv.org/abs/2509.07316 |