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

Abstract

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