On transposed Poisson conformal algebras

TL;DR

This paper introduces noncommutative transposed Poisson conformal algebras, explores their properties, relationships with other algebraic structures, and provides classifications over certain Lie conformal algebras.

Contribution

It defines a new class of conformal algebras, studies their tensor products, relationships with Hom-Lie conformal algebras, and classifies structures over W(a, b).

Findings

Tensor product of two transposed Poisson conformal algebras is also transposed Poisson.

Established a relationship between transposed Poisson and Hom-Lie conformal algebras.

Provided classifications of structures over W(a, b).

Abstract

The aim of this paper is to introduce the notion of (noncommutative) transposed Poisson conformal algebras, which serve as the conformal analogues of transposed Poisson algebras and admit a rich class of identities. We show that the tensor product of two transposed Poisson conformal algebras is also a transposed Poisson conformal algebra. Moreover, we establish a close relationship between transposed Poisson conformal algebras and Hom-Lie conformal algebras, and give the compatibility conditions between a Poisson conformal algebra and a transposed Poisson conformal algebra. In addition, we provide several constructions of transposed Poisson conformal algebras arising from related algebraic structures. Finally, a complete classification of compatible noncommutative transposed Poisson conformal algebraic structures over a class of Lie conformal algebras W(a, b) is given.