Classification of compatible left-symmetric conformal algebraic structures on the Lie conformal algebra $\mathcal{W}(a,b)$

TL;DR

This paper classifies compatible left-symmetric conformal algebraic structures on the Lie conformal algebra W(a,b) and explores their implications for the coefficient algebra.

Contribution

It provides a complete classification of compatible structures on W(a,b), advancing understanding of conformal algebraic structures.

Findings

Complete classification under natural conditions

Identification of compatible structures on coefficient algebra

Extension of results to algebraic structures related to W(a,b)

Abstract

In this paper, under some natural condition, a complete classification of compatible left-symmetric conformal algebraic structures on the Lie conformal algebra $\mathcal{W}(a,b)$ is presented. Moreover, applying this result, we obtain a class of compatible left-symmetric algebraic structures on the coefficient algebra of $\mathcal{W}(a,b)$.