Another class of simple graded Lie conformal algebras that cannot be embedded into general Lie conformal algebras

Abstract

In a previous paper by the authors, we obtain the first example of a finitely freely generated simple $\mathbb{Z}$-graded Lie conformal algebra of linear growth that cannot be embedded into any general Lie conformal algebra. In this paper, we obtain, as a byproduct, another class of such Lie conformal algebras by classifying $\mathbb{Z}$-graded simple Lie conformal algebras $\mathcal{G}={\oplus }_{i=-1}^{\infty }{\mathcal{G}}_i$ satisfying the following, (1) ${\mathcal{G}}_0\cong \mathrm{Vir}$, the Virasoro conformal algebra; (2) Each ${\mathcal{G}}_i$ for $i\ge -1$ is a $\mathrm{Vir}$-module of rank one. These algebras include some Lie conformal algebras of Block type.

References in corpus (1)

• Loop Virasoro Lie Conformal Algebra