Journal of Algebra | 2021
Another class of simple graded Lie conformal algebras that cannot be embedded into general Lie conformal algebras
Abstract
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=−1Gi 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.