BiHom-(pre-)Poisson conformal algebra

TL;DR

This paper introduces and develops the theory of BiHom-Poisson conformal algebras, including their constructions, representations, and related operators, expanding the algebraic framework for conformal algebra structures.

Contribution

It defines BiHom-Poisson conformal and pre-Poisson conformal algebras, explores their properties, constructions, and representation theory, and studies associated operators like Rota-Baxter and $ ext{O}$-operators.

Findings

Construction of new BiHom-Poisson conformal algebras from existing ones

Tensor product of two BiHom-Poisson conformal algebras is also a BiHom-Poisson conformal algebra

Development of the representation theory and operator theory for these algebras

Abstract

The aim of this study is to introduce the notion of BiHom-Poisson conformal algebra, BiHom-pre-Poisson conformal algebra, and their related structures. We show that we can construct many new BiHom-Poisson conformal algebras for a given BiHom-Poisson conformal algebra. Moreover, the tensor product of two BiHom-Poisson conformal algebras is also a BiHom-Poisson conformal algebra. We further describe the conformal bimodule and representation theory of BiHom-Poisson conformal algebra. In addition, we define BiHom-pre-Poisson conformal algebra as the combination of BiHom-preLie conformal algebra and BiHom-dendriform conformal algebra under some compatibility conditions. We also demonstrate that how to construct BiHom-Poisson conformal algebra from BiHom-pre-Poisson conformal algebra and provide the representation theory for BiHom-pre-Poisson conformal algebra. Finally, a detailed description of $\mathcal{O}$-operators and Rota-Baxter operators on BiHom-Poisson conformal algebra is provided.