A class of uniformly bounded simple $\mathbb{Z}$-graded Lie conformal algebras

TL;DR

This paper classifies a specific class of simple, uniformly bounded, $bZ$-graded Lie conformal algebras with rank constraints and a Virasoro algebra component, expanding understanding of their structure.

Contribution

It provides a complete classification of simple $bZ$-graded Lie conformal algebras with bounded rank and a Virasoro subalgebra, which was previously unknown.

Findings

Identified all such simple $bZ$-graded Lie conformal algebras.

Established the structure and properties of these algebras.

Extended the theory of Lie conformal algebras with new classifications.

Abstract

In this paper, we classify the following simple $\mathbb{Z}$-graded Lie conformal algebras $\mathcal{L}=\bigoplus_{i\in \mathbb{Z}}\mathcal{L}_i$ such that (1)$rank\mathcal{L}_i\leq 1$, (2)$\mathcal{L}_0$ is the Virasoro Lie conformal algebra.