2025/09/09 by Atef Hajjaji, Hajjaji, Atef, Lamei Yuan +1
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2509.07316
In this paper, we introduce the concept of L-dendriform conformal algebras, which arise naturally from the study of 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 O -operators, Rota-Baxter operators, and Nijenhuis operators, and demonstrate their connections to dendriform and quadri conformal algebras. Additionally, we investigate compatible 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.