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 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 Z-graded simple Lie conformal algebras G=⊕i=−1∞Gi satisfying the following,(1)G0≅Vir, the Virasoro conformal algebra;(2)Each Gi for i≥−1 is a Vir-module of rank one. These algebras include some Lie conformal algebras of Block type.